Spatio-temporal processing for communication

ABSTRACT

A space-time signal processing system with advantageously reduced complexity. The system may take advantage of multiple transmitter antenna elements and/or multiple receiver antenna elements, or multiple polarizations of a single transmitter antenna element and/or single receiver antenna element. The system is not restricted to wireless contexts and may exploit any channel having multiple inputs or multiple outputs and certain other characteristics. Multi-path effects in a transmission medium cause a multiplicative increase in capacity.

STATEMENT OF RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 11/052,978 filed Feb. 7, 2005. U.S. patent application Ser. No.11/052,978 in turn is a continuation of U.S. patent application Ser. No.10/172,373 filed Jun. 13, 2002 (now U.S. Pat. No. 6,888,899) which inturn is a continuation of U.S. patent application Ser. No. 09/435,293filed Nov. 5, 1999 (now U.S. Pat. No. 6,452,981) which in turn is acontinuation of U.S. patent application Ser. No. 08/921,633 filed Aug.27, 1997 (now U.S. Pat. No. 6,144,711). The contents of each of U.S.patent application Ser. Nos. 11/052,978, 10/172,373, 09/435,293, and08/921,633 are herein incorporated by reference for all purposes.

The present application claims priority from two provisionalapplications: SPATIO-TEMPORAL CODING FOR WIRELESS COMMUNICATION, U.S.Prov. App. No. 60/025,227 and SPATIO-TEMPORAL CODING TECHNIQUES FORRAPIDLY FADING WIRELESS CHANNELS, U.S. Prov. App. No. 60/025,228, bothfiled on Aug. 29, 1996. The contents of both provisional applicationsare herein incorporated by reference for all purposes.

BACKGROUND OF THE INVENTION

The present invention relates to digital communication and moreparticularly to a space-time communication system.

The ability to communicate through wireless media is made difficult bythe inherent characteristics of how transmitted signals propagatethrough the environment. A communication signal transmitted through atransmitter antenna element travels along multiple paths to thereceiving antenna element. Depending on many factors including thesignal frequency and the terrain, the paths along which the signaltravels will exhibit different attenuation and propagation delays. Thisresults in a communication channel which exhibits fading and delayspread.

It is well known that adaptive spatial processing using multiple antennaarrays increases the communications quality of wireless systems.Adaptive array processing is known to improve bit error rate, data rate,or spectral efficiency in a wireless communication system. The prior artprovides for methods involving some form of space-time signal processingat either the input to the channel, the output to the channel, or both.The space-time processing step is typically accomplished using anequalization structure wherein the time domain equalizer tap settingsfor a multitude of antennas are simultaneously optimized. This so-called“space-time equalization” leads to high signal processing complexity ifthe delay spread of the equivalent digital channel is substantial.

There is prior art teaching the use of conventional antenna beams orpolarizations to create two or more spatially isolated communicationchannels between a transmitter and a receiver, but only under certainfavorable conditions. The radiation pattern cross talk between differentphysical transmit and receive antenna pairs must provide sufficientspatial isolation to create two or more substantially independentcommunication channels. This can lead to stringent manufacturing andperformance requirements on the physical antenna arrays as well as thereceiver and transmitter electronics. In addition, when large objects inthe wireless propagation channel cause multipath reflections, thespatial isolation provided by the prior art between any two spatialsubchannels can be severely degraded, thus reducing communicationquality.

What is needed is a system for more effectively taking advantage ofmultiple transmitter antennas and/or multiple receiver antennas toameliorate the deleterious effects of the inherent characteristics ofwireless media.

SUMMARY OF THE INVENTION

The present invention provides a space-time signal processing systemwith advantageously reduced complexity. The system may take advantage ofmultiple transmitter antenna elements and/or multiple receiver antennaelements, or multiple polarizations of a single transmitter antennaelement and/or single receiver antenna element. The system is notrestricted to wireless contexts and may exploit any channel havingmultiple inputs or multiple outputs and certain other characteristics.In certain embodiments, multi-path effects in a transmission mediumcause a multiplicative increase in capacity.

One wireless embodiment operates with an efficient combination of asubstantially orthogonalizing procedure (SOP) in conjunction with aplurality of transmitter antenna elements with one receiver antennaelement, or a plurality of receiver antenna elements with one transmitantenna element, or a plurality of both transmitter and receiver antennaelements. The SOP decomposes the time domain space-time communicationchannel that may have inter symbol interference (ISI) into a set ofparallel, space-frequency, SOP bins wherein the ISI is substantiallyreduced and the signal received at a receiver in one bin of the SOP issubstantially independent of the signal received in any other bin of theSOP. A major benefit achieved thereby is that the decomposition of theISI-rich space time channel into substantially independent SOP binsmakes it computationally efficient to implement various advantageousspatial processing techniques embodied herein. The efficiency benefit isdue to the fact that the total signal processing complexity required tooptimize performance in all of the SOP bins is often significantly lowerthan the processing complexity required to jointly optimize multipletime domain equalizers.

Another benefit is that in many types of wireless channels where therank of the matrix channel that exist between the transmitter and thereceiver within each SOP bin is greater than one, the combination of anSOP with spatial processing can be used to efficiently provide multipledata communication subchannels within each SOP bin. This has thedesirable effect of essentially multiplying the spectral data efficiencyof the wireless system. A further feature is the use of spatialprocessing techniques within each transmitter SOP bin to reduce radiatedinterference to unintentional receivers. A still further feature is theability to perform spatial processing within each receiver SOP bin toreduce the deleterious effects of interference from unintentionaltransmitters.

One advantageous specific embodiment for the SOP is to transmit withIFFT basis functions and receive with FFT basis functions. Thisparticular SOP is commonly referred to as discrete orthogonal frequencydivision multiplexing (OFDM), and each SOP bin is thus associated with afrequency bin. This embodiment enhances OFDM with the addition ofefficient spatial processing techniques.

According to the present invention, space-frequency processing mayadaptively create substantially independent spatial subchannels withineach SOP bin even in the presence of significant cross talk interferencebetween two or more physical transmit and receive antenna pairs. Afurther advantage is that the space-frequency processing canadvantageously adapt to cross talk interference between the physicalantenna pairs even if this cross-talk is frequency dependent, or timevarying, or both. Thus, the present invention may provide two or moresubstantially independent communication channels even in the presence ofsevere multipath and relatively poor physical antenna radiation patternperformance.

A further understanding of the nature and advantages of the inventionsherein may be realized by reference to the remaining portions of thespecification and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a transmitter system according to one embodiment of thepresent invention.

FIG. 2 depicts a particular substantial orthogonalizing procedure (SOP)useful in one embodiment of the present invention.

FIG. 3 depicts a receiver system according to one embodiment of thepresent invention.

FIG. 4 depicts a first communication scenario where multipath is found.

FIG. 5 depicts a second communication scenario where multipath is found.

FIG. 6 depicts a third communication scenario where multipath is found.

FIG. 7 depicts a multiple-input, multiple-output (MIMO) channel withinterference.

FIG. 8 depicts the use of an SOP in a single-input single-output (SISO)channel.

FIG. 9 depicts the use of an SOP in a MIMO channel according to oneembodiment of the present invention.

FIG. 10 depicts the operation of an SOP in the context of one embodimentof the present invention.

FIG. 11 depicts the application of spatial processing to a particularSOP bin at the transmitter end according to one embodiment of thepresent invention.

FIG. 12 depicts the application of spatial processing to a particularSOP bin at the receiver end according to one embodiment of the presentinvention.

FIG. 13 depicts the application of spatial processing to N SOP bins atthe transmitter end according to one embodiment of the presentinvention.

FIG. 14 depicts the application of spatial processing to N SOP bins atthe receiver end according to one embodiment of the present invention.

FIG. 15 depicts the use of a single spatial direction at the transmitterend for each bin of an SOP according to one embodiment of the presentinvention.

FIG. 16 depicts the use of a single spatial direction at the receiverend for each bin of an SOP according to one embodiment of the presentinvention.

FIG. 17 depicts the use of one or more common spatial weighting vectorsfor all SOP bins at the transmitter end according to one embodiment ofthe present invention.

FIG. 18 depicts the use of one or more common spatial weighting vectorsfor all SOP bins at the receiver end according to one embodiment of thepresent invention.

FIG. 19 depicts the use of an encoder for each SOP bin according to oneembodiment of the present invention.

FIG. 20 depicts the use of an encoder for each spatial directionaccording to one embodiment of the present invention.

FIG. 21 depicts the use of an encoder for each space/frequencysubchannel according to one embodiment of the present invention.

FIG. 22 depicts distribution of encoder output over all space/frequencysubchannels according to one embodiment of the present invention.

FIG. 23 depicts a detailed diagram of an encoder/interleaver systemaccording to one embodiment of the present invention.

FIG. 24 depicts a transmitter system wherein multiple space/frequencysubchannels are employed without spatial orthogonalization according toone embodiment of the present invention.

FIG. 25 depicts a receiver system wherein multiple space/frequencysubchannels are employed without spatial orthogonalization according toone embodiment of the present invention.

FIG. 26 depicts an exemplary technique for bit loading with a trelliscoder that uses a one-dimensional QAM symbol constellation.

DESCRIPTION OF SPECIFIC EMBODIMENTS

Definitions

A “channel” refers to the input symbol to output symbol relationship fora communication system. A “vector channel” refers to a channel with asingle input and multiple outputs (SIMO), or multiple inputs and asingle output (MISO). Each h_(j) entry in the vector channel h describesone of the complex path gains present in the channel. A “matrix channel”refers to a channel with multiple inputs and multiple outputs (MIMO).Each entry H_(i,j) in the matrix H describes the complex path gain frominput j to output i. A “space time channel” refers to the input tooutput relationship of a MIMO matrix channel, or a SIMO or MISO vectorchannel, that occurs when multipath signal propagation is present sothat the channel contains delay elements that produce inter-symbolinterference (ISI) as explained below.

A “spatial direction” is a one dimensional subspace within a matrix orvector communication channel. Spatial directions need not be orthogonal.A spatial direction is typically characterized by a complex input vectorand a complex output vector used to weight transmitted or receivedsignals as explained herein.

A “sub-channel” is a combination of a bin in a substantiallyorthogonalizing procedure (SOP) as explained below and a spatialdirection within that bin. A group of spatial subchannels within an SOPbin may or may not be orthogonal.

An “orthogonal dimension” is one member in a set of substantiallyorthogonal spatial directions.

A channel “subspace” is a characterization of the complex m-spacedirection occupied by one or more m-dimensional vectors. The subspacecharacterization can be based on the instantaneous or average behaviorof the vectors. A subspace is often characterized by a vector-subspaceof a covariance matrix. The covariance matrix is typically a time orfrequency averaged outer product of a matrix or vector quantity. Thecovariance matrix characterizes a collection of average channeldirections and the associated average strength for each direction.

A “two norm” metric for a vector is the sum of the squared absolutevalues for the elements of the vector.

A “Euclidean metric” is a two norm metric.

“Intersymbol interference” (ISI) refers to the self interference thatoccurs between the delayed and scaled versions of one time domain symboland subsequent symbols received at the output of a delay spreadcommunication channel. The channel delay spread is caused by thedifference in propagation delay between the various multipath componentscombined with the time domain response of the RF and digital filterelements.

A “substantially orthogonalizing procedure” (SOP) is a procedure thatplays a part in transforming a time domain sequence into a parallel setof substantially orthogonal bins, wherein the signals in one bin do notsubstantially interfere with the signals from other bins. Typically, thetransformation from a time domain sequence to a set of substantiallyorthogonal bins requires a transmitter SOP with a set of input bins, anda receiver SOP with a set of output bins.

“Convolutional bit mapped QAM” (CBM-QAM) is the coding system thatresults when the output of a convolutional encoder are grouped andmapped to QAM constellation points.

Fading “structure” occurs when the fading behavior of one or moreentries in a channel matrix within an SOP bin is correlated across time,or frequency, or both. This structure can be exploited usingadvantageously designed estimation filters to improve channel estimationaccuracy given multiple frequency samples of the channel matrix entries,or multiple time samples, or both.

A “maximum likelihood sequence detector” is a sequence estimator thatcomputes the most likely transmitted code sequence, from a set ofpossible sequences, by minimizing a maximum likelihood cost function.

An “antenna element” is a physical radiator used to transmit or receiveradio frequency signals. An antenna element does not involve anyelectronics processing components. A single radiator with twopolarization feeds is viewed as two antenna elements.

An “antenna array” is a collection of antenna elements.

A “burst” is a group of transmitted or received communication symbols.

Background Material

The disclosure herein assumes a background in digital communication andlinear algebra. The following references are incorporated herein byreference.

Wozencraft & Jacobs, Principles of Communication Engineering (1965).

Haykin, Adaptive Filter Theory, 2nd Ed. (1991).

Strang, Linear Algebra, 3^(rd) Ed. (1988).

Jakes, Microwave Mobile Communication (1974).

Proakis, Digital Communications (1995).

Transmitter Overview

FIG. 1 depicts a transmitter system in accordance with one embodiment ofthe present invention. Typically an information signal input 2 includesa digital bit sequence, although other forms of digital data or analogdata are possible. In the case of digital data, the input data sequenceis first fed into an Encoder and Interleaving apparatus 10 where thedata is encoded into a symbol stream. The symbol stream is typically asequence of complex digitized values that represent members of a finiteset. Each symbol can be a one dimensional value, or a multidimensionalvalue. An exemplary one dimensional symbol set is a PAM constellation.Note that in this discussion, it is understood that a symbol within-phase and quadrature components, is considered to be a complex onedimensional symbol, so that the QAM constellation is also viewed as aset of one dimensional symbols. An example multidimensional symbol setis a sequential grouping of QAM constellation members.

The purpose of the encoding process is to improve the bit error rate ofthe transmitted signal by introducing some form of informationredundancy into the transmitted data stream. Useful encoding techniquescan involve combinations of a number of well known techniques such asconvolutional encoding with bit mapping to symbols, trellis encoding,block coding such as cyclic redundancy check or Reed Solomon coding withbit mapping or Automatic Repeat Queing. An interleaver is oftenadvantageous for distributing the transmitted information among thevarious subchannels available for transmission. This interleavingdistributes the effects of channel fading and interference so that longsequences of symbols with poor quality are not grouped closely togetherin the SOP bin sequence that is fed into the receiver decoder. In manyapplications, it is advantageous to perform a power and bit-loadingoptimization wherein the number of bits that are mapped to a givenencoder symbol, and the signal power assigned to that symbol, aredetermined based upon the measured communication quality of thespace-frequency information subchannel that carries the symbol stream.

After the digital data is encoded into a sequence of symbols, a TrainingSymbol Injection block 20 may be used to place a set of known trainingsymbol values in the transmitter symbol stream. The purpose of thetraining symbols is to provide a known input within a portion of thetransmitted symbol stream so that a receiver may estimate thecommunication channel parameters. The channel estimate is used to aid indemodulation and decoding of the data sequence. The training symbols maybe injected periodically in time, periodically in frequency, or both. Itwill be obvious to one skilled in the art that blind adaptive spatialprocessing techniques can be utilized within each SOP bin at thereceiver as an alternative to training with known symbols. In such blinddetection implementations, Training Symbol Injection block 20 isunnecessary.

The data plus training symbol stream is then fed into a TransmitterSpace-Frequency Pre-Processor (TSFP) block 30. The TSFP block 30performs two sets of advantageous processing steps on the symbol streambefore transmission. One processing step accomplished within the TSFP isthe transmitter portion of a substantially orthogonalizing procedure(SOP). When the transmitter portion of the SOP is combined with thereceiver portion of the SOP, a set of parallel bins are created in sucha manner that information transmitted within one bin does notsubstantially interfere with information transmitted from another binafter the receive portion of the SOP is completed. One preferred SOPpair is the inverse fast Fourier transform (IFFT) at the transmittercombined with the FFT at the receiver. Another advantageous SOP pairembodiment is a bank of multiple filter and frequency converter pairs(multi-band SOP) with one filter bank located at the transmitter and onefilter bank located at the receiver as depicted in FIG. 2. Several otherexample SOPs including the Hilbert transform pair and generalizedwavelet transform pairs will be obvious to one skilled in the art. Theother processing step accomplished in the TSFP is spatial processing.The spatial processing step typically multiplies one or more symbolsthat are destined for transmission in a given SOP bin with one or morespatial vector weights. For convenience in the following discussion, thecollection of spatial processing weights applied to the signalstransmitted or received in a given SOP bin are sometimes referred to asa matrix. The spatial vector weights are optimized to obtain variousdesirable performance enhancements.

FIG. 2 depicts a digital baseband filter bank at the receiver and afilter bank located at the transmitter. Each filter of the transmitterfilter bank includes a mixer (frequency converter) 60, a bandpass filter70 and an interpolator 80. Each filter of the receiver filter bankincludes a bandpass filter 90, a mixer 60, and a decimator 100.

One transmitter embodiment optimizes the transmitter spatial vectorweights so that the multiple subchannels in a given SOP bin can beconverted at the receiver into substantially independent receivedspatial subchannels wherein symbols from one subchannel do notsubstantially interfere with symbols from another subchannel. Anotherembodiment optimizes the transmitter spatial vector weight to improvethe received power of one or more spatial subchannels within each SOPbin, or to improve the average power of several spatial subchannelswithin several SOP bins. A further embodiment optimizes the transmitterspatial vector weights within each SOP bin to simultaneously increasethe power delivered to the desired receiver within one or more spatialsubchannels while reducing interference radiated to unintendedreceivers. A yet further embodiment spatial processes one or moresymbols within each SOP bin by multiplying each symbol with atransmitter weight vector that is fixed for all SOP bins, with theweight vectors optimized to increase the time or frequency average powerdelivered to one or more desired receiver spatial subchannels, andpossibly reduce the time or frequency averaged interference radiated tounintended receivers. This last embodiment is particularly useful in FDDsystems where multipath fading makes it impossible to estimate theforward channel from reverse channel data, but where the average forwardchannel subspaces are substantially similar to the average reversechannel subspaces. Another embodiment teaches simply routing each symbolfrom the encoder to one antenna element in each SOP bin without anyweighting. Other useful embodiments are discussed herein, and manyothers useful combinations of spatial processing with an SOP will becomeobvious to one skilled in the art. It is understood that one or moredigital filters are typically used in TSFP 30 to shape the transmittedRF signal spectrum.

Once the encoder symbol sequence is processed by TSFP 30, the processedsymbol sequence includes a parallel set of digital time domain signalsequences. Each of these time domain signal sequences is fed into oneinput of a Modulation and RF System block 40. Modulation and RF Systemblock 40 includes a set of independent RF upconverter chains thatfrequency convert the digital baseband signal sequence up to the RFcarrier frequency. This is accomplished using apparatus that includesdigital to analog converters, RF mixer apparatus, and frequencysynthesizer apparatus. The details of these elements of the inventionare well known and will not be discussed here.

The final step in the transmission process is to radiate the transmittedsignal using a Transmit Antenna Array 50. The antenna arrays can beconstructed from one or more co-polarized radiating elements or theremay be multiple polarizations. If there is multipath signal propagationpresent in the radio link, or if there are multiple polarizations in theantenna arrays, or if at least one of the antenna elements on one sideof the link are in a disparate location from the other elements on thesame side of the link, then the invention has the advantageous abilityto create more than one subchannel within each SOP bin. It is understoodthat one physical antenna reflector with a feed that has twopolarizations is considered as two antenna elements in all that follows.There are no restrictions on the antenna array geometry or the geometryof each radiating element. A transmitter system invention may adapt toprovide optimized performance for any arbitrary antenna array.

Receiver Overview

FIG. 3 depicts a receiver system according to one embodiment of thepresent invention. The RF signals from each of the elements of anAntenna Array 110 are downconverted to digital baseband using aDemodulation and RF System 120. Demodulation and RF System 120 includesthe RF signal processing apparatus to downconvert the RF carrier signalto a baseband IF where it is then digitized. After the digitizer, atiming and frequency synchronization apparatus is used to recover thetiming of the transmitted digital signal sequence. Several knowntechniques may be used for the purpose of synchronization and thesetechniques will not be discussed herein.

In certain embodiments of the invention, after Demodulation and RFSystem 120, the digital baseband signal is then fed into a Channel IDblock 130 and a Receiver Space-Frequency Processor (RSFP) block 140.Within Channel ID block 130, the characteristics of the digitalcommunication channel are estimated. The estimated channel valuesconsist of entries in a matrix for each SOP bin. The matrix containscomplex values representing the magnitude of the spatial channel withinthe SOP bin from one transmit antenna element to one receive antennaelement. The matrix channel estimate for each SOP bin is provided toRSFP block 140 and Decoder and Deinterleaving block 150.

Some embodiments of the invention involve improving channel estimationperformance by exploiting the structured nature of the frequency domainfading that exists in the matrix channels across SOP bins, exploitingthe structure in time domain fading of the matrix channels, orexploiting both the frequency and time domain fading structure that ispresent. By exploiting the frequency domain fading correlation, theentire set of matrix channels within the SOP bins may be estimated evenwhen training information is transmitted in a subset of the SOP bins.This allows for simultaneous transmission of training and data thusreducing overhead. By exploiting the time domain correlation of thechannel fading within each SOP bin, channel estimation accuracy isincreased for a given time epoch between training events. This reducesthe required frequency of training symbol transmission and thus furtherreduces training overhead. It is understood that it is also possible toseparately exploit time domain and frequency domain correlation, withthe most beneficial results occurring if both correlation dimensions areused advantageously. It is to be understood that Channel ID block 130 isshown as a separate function even though it may share some elements withRSFP block 140 or Decoder and Deinterleaver block 150.

RSFP block 140 performs the receiver signal processing that is the dualof the two sets of operations performed in TSFP 30. One of the stepsperformed in RSFP 140 is the receiver half of the SOP. As discussedabove, the receiver half of the SOP completes the transformation betweenthe time domain channel with ISI to the substantially orthogonal set ofbins. The second set of signal processing operations that can beperformed in the RSFP is spatial processing. In one class ofembodiments, the receiver spatial processing step combines the output ofthe SOP bins using one or more vector weighted inner product steps toform one or more one-dimensional received spatial subchannels withineach SOP bin. The receiver weight vectors are chosen to optimize anadvantageous performance measure. In one embodiment, wherein both thetransmitter and receiver have knowledge of the channel state informationwithin each SOP bin, the transmitter spatial weight vectors and thereceiver spatial weight vectors are both chosen to optimize performancefor a set of multiple substantially independent subchannels within eachSOP bin. As discussed above, this significantly increases the spectralefficiency of the system. In another embodiment wherein the transmitterdoes not have channel state information, the receiver performs thespatial processing required to create multiple substantially independentsubchannels within each SOP bin. In a further embodiment wherein thetransmitter may or may not have channel state information, the receiverreduces the effects of interference radiated from unintentionaltransmitters as well as performing the spatial processing required tocreate multiple substantially independent subchannels within each SOPbin. A yet further embodiment optimizes the receiver spatial vectorweights within each SOP bin to simultaneously increase the receivedpower and reduce the detrimental effects of interference received fromunintentional transmitters. An additional embodiment involves formingone or more vector weights, that are fixed for all SOP bins, where thevector weights are optimized to simultaneously increase the time orfrequency averaged received power for one or more spatial subchannels,while possibly also reducing the time or frequency averaged interferencepower received from unintended transmitters.

As discussed herein, certain embodiments involve simply passing thevector samples received in each SOP bin to Decoder and Deinterleavingblock 150 without performing any spatial processing. It will be obviousto one skilled in the art that other combinations of transmitter spatialweight vector optimization techniques and receiver spatial weight vectoroptimization techniques can be constructed around the principle conceptof spatial processing in combination with an SOP. Other embodiments arediscussed herein. One experienced in the art will be able to recognizeadditional embodiments that involve advantageous combination of an SOPwith spatial processing at the receiver or the transmitter. It isunderstood that one or more digital filters are typically used in RSFPblock 1400 to shape the received RF signal spectrum.

The outputs of RSFP block 140 are fed into Decoder and Deinterleaving(DD) block 150. There are two broad exemplary classes of operation forthe DD block 150. In the first exemplary broad class of embodiments, DDblock 150 decodes a symbol sequence which was encoded and transmittedthrough a multitude of SOP bins with one or more substantiallyindependent subchannels. The decoder includes the appropriate receivercounterparts for the combination of encoders selected for thetransmitter. A preferred embodiment includes a deinterleaver, a trellisdecoder or convolutional bit mapping decoder employing a scalar weightedEuclidean maximum likelihood sequence detector, followed by a ReedSolomon decoder, followed by an ARQ system to correct Reed Solomoncodeword errors. In the second exemplary broad class of embodiments, DDblock 150 decodes a sequence of multidimensional symbols, or groups ofadjacent one dimensional symbols, with each multidimensional symbol orgroup of one dimensional symbols being received in an SOP bin.Typically, the symbol sequences are transmitted without weighting orwith weighting that optimizes some measure of average signal quality.

In an alternative embodiment, trellis encoded symbols are grouped andinterleaved in a manner such that the symbols transmitted from theantenna elements within a given SOP bin form a vector that is drawn fromeither a multidimensional QAM encoder output symbol, or a sequence ofone dimensional QAM encoder output symbols that have adjacent locationsin the pre-interleaved encoder output sequence. In this way, a maximumlikelihood vector decoder may be constructed given an estimate of thechannel matrix that is present within each SOP bin. The maximumlikelihood decoder computes the weighted vector Euclidean metric giventhe deinterleaved received vector from each SOP bin, the deinterleavedmatrix channel estimates from each SOP bin, and the transmitted vectorsymbol trellis state table.

In another alternative embodiment, either of the aforementioned encoderembodiments will have preferable performance if the encoder polynomialand symbol constellation set are optimized to improve the bit error rateperformance given the characteristics of the matrix channel fading thatoccurs in each SOP bin. One particular metric that is well suited for acode polynomial optimization search is the product of the two norms ofthe vector difference between the correct transmitter symbol vector andthe error symbol vector.

The output of DD block 150 is the estimated bit stream at the receiveend of the radio link.

It is to be understood that all transmitter embodiments of the presentinvention may be adapted for use with a receiver accessing the channelthrough a single channel output such as a single receiver antennaelement. Furthermore, all receiver embodiments of the present inventionmay be adapted for use with a transmitter accessing the channel througha single channel input such as a single transmitter antenna element. Itis understood that the channel is then a vector channel. Suchmultiple-input single-output (MISO) and single-input multiple output(SIMO) systems are within the scope of the present invention.

Space-Frequency Communication in a Multipath Channel

Before developing the signal processing of the present invention, aphysical description and mathematical description of wireless channelsare provided. Many wireless communication channels are characterized bymulti-path, where each path has associated fading and propagation delay.Multipath may be created by reflections in the physical radio path,multiple antenna polarizations, antenna elements located in disparatelocations, or a combination of any of these. One scenario in whichmultipath is created is illustrated in FIG. 4. A Base 152 transmitsinformation to and receives information from a remote unit 170A or 170B.Base 152 possesses one or more antenna elements referred to as an array55. Similarly, the Remote Units possess their own arrays 55. Atransmitted signal propagates along multiple paths 155A-C created byreflection and scattering from physical objects in the terrain 160A-D.

Multipath signal propagation such as that depicted in FIGS. 4-6 can giverise to spatially selective fading, delay spread, frequency fading, andtime fading. Spatial fading occurs as the various wavefronts arriving atthe receiver from different propagation paths combine with constructiveand destructive interference at different points in space. An antennaarray located within this spatially selective field will sample thefield at various locations so that the signal strength at each arrayelement is different. Delay spread occurs due to the differingpropagation path lengths. The channel delay spread gives rise to afrequency selective digital communication channel at each antennaelement. This frequency response is different for each antenna elementby virtue of the frequency dependent spatial fading. Finally, if eitherthe transmitter, or the receiver, or objects in the terrain are moving,the frequency selective spatial fading will vary as a function of time.The present invention is unique in that it is capable of efficiently andeconomically adapting to the time varying space-frequency channelresponse to make advantageous use of the inherent properties of suchchannels.

For several decades, the primary focus of the prior art has been tosomehow mitigate the effects of the multipath channel. This conventionalapproach is ill-advised since multipath channels give rise to amultiplicative capacity effect by virtue of the fact that the multipathinduces a rank greater than one in the matrix channel present in eachSOP bin. This provides opportunity to form multiple parallel subchannelsfor communication within each SOP bin. Thus, one should utilizemultipath to improve communication performance rather than attempt tomitigate its effects. A substantial advantage provided by the presentinvention is the ability to efficiently and economically exploit theinherent capacity advantages of multipath channels using a combinationof an SOP and spatial processing or spatial coding. No other structuresare known to efficiently exploit this fundamental advantage in thepresence of substantially frequency selective multipath channels.

FIG. 5 illustrates another wireless channel scenario in which multipathis present. A Base 152 with an antenna array 55 transmits information toand receives information from a Remote 170C with an antenna array 55. Inthis case, both Base and Remote antenna arrays 55 both have elementswith differing polarizations. Thus multipath signal propagation existseven if there are no significant reflections in the physicalenvironment. The direct line of sight paths 155B, 155E eachcorresponding to one of the polarizations in the array elements, aresufficient to create a matrix channel with a rank greater than onewithin each SOP bin, even if the other reflected radio paths 155A, 155C,155D, and 155F are insignificant or nonexistent.

It is known that such line of sight polarization (reflection free)channels can be decomposed into two parallel communication channels byusing high performance dual polarization antennas, one at each end ofthe radio link, in combination with high performance receiver andtransmitter electronics apparatus. In this prior art, the quality of theparallel communication channels is limited by the degree to which thetwo polarization channels remain independent. In general, maintainingthe manufacturing tolerances and installation alignment precision in theantennas and electronics required to achieve substantially orthogonalspatial subchannels at the output of the physical receive antenna isrelatively expensive. Slight manufacturing errors and componentvariations can lead to a significant cross-talk interference between themultiple polarizations present in the radio channel. In contrast, anadvantageous feature of the invention is that the differentpolarizations present in the wireless channel may have an arbitrarydegree of cross-talk interference, and the cross-talk interference maybe frequency dependent without loss of performance. In such cases, theinvention provides an economical and efficient method for fullyexploiting the multi-dimensional nature of the multiple polarizationchannel. It is understood that the invention can provide furthercapacity advantage if the multiple polarization channel also hasreflected signal paths. This additional multipath results in anadditional increase in the channel matrix rank in each SOP bin that canbe further exploited to improve the capacity of the channel.

FIG. 6 depicts another wireless communication scenario in whichmultipath is present and can be exploited to create multiple dimensionsfor communication. In FIG. 6, two Bases 152A and 152B with antennaarrays 55 communicate with Remote Units 170A and 170B that also possessantenna arrays 55. In this case, the composite channel is defined as theMIMO channel between the antennas of the two Bases 152A and 152B and theantennas of the Remote Units 170A and 170B. Note that this channelincludes direct line of sight paths 155B and 153B as well as thereflected paths 155A, 155C, 153A, 153C, and 153D. By virtue of thespatial separation between two Bases 152A and 152B, even if thereflected paths are insignificant or nonexistent, this channel containsmultipath that can be exploited using the invention. In addition, thechannel from the antennas of the two Bases to the antennas of one Remoteis again a matrix channel, with rank greater than one, within each SOPbin so that multiple parallel dimensions for transmission may becreated. In these types of applications, the present invention providesfor the ability to reduce interference radiate to unintentionalreceivers. Furthermore, the present invention provides the capability ofreducing the detrimental effects of received interference fromunintentional transmitters.

Thus it can be seen that multiple transmitter antenna elements ormultiple antenna elements may be either co-located or be found atdisparate locations.

The following symbol channel model applies to all of the above multipathradio propagation cases illustrated by FIGS. 4-6. The channel impulseresponse includes the effects of the propagation environment, as well asthe digital pulse shaping filters used in TSFP 30 and RSFP 140, theanalog filters used in Modulation & RF System 40 and Demodulation & RFSystem 120. Due to the difference in propagation delay between thevarious multipath components combined with the time domain response ofthe RF and digital filter elements, a single symbol transmitted into thechannel is received as a collection of delayed copies. Thus, delayed andscaled versions of one symbol interfere with other symbols. This selfinterference effect is termed intersymbol interference or ISI. The delayspread parameter, denoted by v, is the duration in symbol periods of thesignificant portion of the channel impulse response.

As the transmitted symbol rate is increased or as the physicalgeometries in the channel become larger, the delay spread can become solarge that conventional space-time processing systems become highlycomplex. An advantage of the present invention is that the signalprocessing complexity is relatively low even when the delay spreadbecomes extremely large. This allows for the economical application ofMIMO space-frequency processing techniques at high digital data rates.This efficient use of signal processing comes about because theinvention allows the space-time channel to be treated as a set ofsubstantially independent spatial subchannels without sacrificingchannel capacity. In contrast, conventional approaches either attempt toequalize the much more complex space-time channel or alternativelysacrifice capacity.

The channel is modeled as time-invariant over the time spanned by aburst of N data symbols, but varying from one burst to another. Thisblock time invariant assumption produces a channel model that issufficiently accurate for channels wherein the block duration is shortcompared to the channel fading, or (N+2v)T<<Δ_(β), where Δ_(β) is thecorrelation interval. Note that the correlation interval here is definedas the time period required for the fading parametertime-autocorrelation function to decrease to some fraction of thezero-shift value. Other models are available wherein the channel variescontinuously, but these models add unnecessary complication to thepresent discussion. It is understood that rapid time variation in thechannel can be another motivation for choosing one of the other SOPalternatives in the presence of fading rates that are rapid with respectto the burst frequency. One skilled in the art will be aware of thepertinent issues for a given application. For example, OrthogonalFrequency Domain Multiplexing (OFDM) is an SOP composed of an IFFT andcyclic prefix as the transmitter SOP, and an FFT as the receiver SOP.With OFDM, one pertinent issue is frequency domain inter-carrierinterference (ICI), which can occur in OFDM systems with extremely rapidfading. Such pertinent issues shape the appropriate choice of channelmodels for various SOP basis functions.

With this background discussion, it can be verified by one skilled inthe art that the relationship between the transmitted burst of basebandsymbols and the received burst of baseband samples may be adequatelyexpressed as the space-time equation,x(k)=G(k)z(k)+I(k),

where the index k represents bursts. The composite channel output forone burst of data, x(k), is written with all time samples appear insequence for every receive antenna 1 to M_(R),x(k)=[x ₁(1) . . . x ₁(N+v−1) . . . x _(M) _(R) (1)x _(M) _(R)(N+v−1)]^(T).

Likewise, the input symbol vector is written,z(k)=[z ₁(1) . . . z ₁(N) . . . z _(M) _(T) (1) . . . z _(M) _(T)(N)]^(T).

The quantity I(k), defined the same as x(k) and z(k), represents bothnoise and interference. The MIMO channel matrix, G(k), is composed ofsingle-input single-output (SISO) sub-blocks, $\begin{matrix}{{G(k)} = {\begin{bmatrix}{G_{1,1}(k)} & \cdots & {G_{1,M_{T}}(k)} \\\vdots & ⋰ & \vdots \\{G_{M_{R},1}(k)} & \cdots & {G_{M_{R},M_{T}}(k)}\end{bmatrix} \in {C^{{NM}_{T} \times {({N + v})}M_{R}}.}}} & (1)\end{matrix}$

Furthermore, each of the SISO sub-blocks, G_(i,j)(k), is a Toeplitzmatrix describing the input-output relationship between the transmittedsymbol burst and the received symbol burst for antenna pair (i,j). ThisMIMO space-time channel is illustrated by FIG. 7, which shows SISOsub-blocks 180A-D and the addition of interference for each receiversample.

Space-Frequency Processing

Embodiments of the present invention uses space-frequency processing ateither the transmitter or receiver, or both, to create effectivecommunication systems in wireless channels. Generally, the processingsubstantially eliminates the ISI caused by the channel correlationacross space (antenna correlation) and time (delay spread). Thisprocessing greatly simplifies the design of the remaining functions thatcomprise a complete communication system, including coding andmodulation. Furthermore, the processing approach is based upon acapacity-achieving structure for the MIMO wireless communicationchannel. Space-frequency processing is composed of one or more of thefollowing: an SOP, a transmit spatial processor, and a receive spatialprocessor.

Substantially Orthogonalizing Procedure

The use of an SOP in a SISO channel is considered first in order toillustrate the invention's ability to eliminate ISI across space andtime. The SOP is composed of signal processing operations implemented atboth the transmit and receive sides of the channel. This is illustratedin FIG. 8 where a Transmitter SOP processor 190 and a Receiver SOPprocessor 200 jointly perform a complete SOP. The SOP ensures that the Ninput symbols, in bin 1 through bin N, are transmitted through thechannel in such a way that each output symbol is substantiallyinfluenced by only the input symbol of the same frequency bin. Forexample, the input symbol in bin 1 is the only symbol to havesubstantial influence on the output symbol value in bin 1.

This concept generalizes to the MIMO system as shown in FIG. 9. For theMIMO system, each transmitter antenna 51 is preceded by one of M_(T)identical Transmitter SOP processors. Likewise, each receiver antenna111 precedes one of M_(R) identical Receiver SOP processors. Hence, theprocessing path for any transmitter-receiver antenna pair contains ajointly performed complete SOP. In other words, there exist M_(R)M_(T)SISO SOPs in the MIMO system. By exploiting the property ofsuperposition, this collection of SISO SOPs comprise a MIMO SOP whereany two symbols communicated in different bins exhibit substantiallyreduced crosstalk, irrelevant of the antennas by which the symbols weretransmitted and received. Therefore, the SOP establishes N substantiallyindependent MIMO spatial channels.

Many different SOP implementations exist, including an IFFT-FFT pair, abank of multiple narrow-band filters, and generalized wavelet transformpairs. One advantageous example of an SOP is the use of a frequencytransform combined with a burst cyclic prefix application procedureprocessor 207, as shown in FIG. 10. There is also a cyclic prefixremoval procedure processor 206 at the receive end. When the frequencytransform is an IFFT-FFT pair 205 and 208 as shown in FIG. 10, thisparticular SOP is commonly referred to as discrete orthogonal frequencydivision multiplexing (OFDM). Hence, this embodiment of the inventioncombines the OFDM SOP with multiple input antennas, or multiple outputantennas, or both multiple input and multiple output antennas. Thepresent embodiment is thus termed matrix-OFDM (MOFDM).

The analysis presented for MOFDM will have a substantially similar formas other choices for the SOP. These alternative embodiments have certainadvantages and drawbacks as compared to the OFDM SOP. For example, themulti-band SOP does not completely eliminate ISI, but it is more robustto certain types of narrow-band interfering signals because theinterference can be more confined within a given SOP bin as compared tothe OFDM SOP. The ISI that can be present in the multi-band SOP couldmake it advantageous to use pre-equalization or post-equalizationstructures in conjunction with the spatial processing within a given SOPbin. While this complicates the spatial processing, the complexitydrawback may be outweighed by other requirements such as robustness tointerference or the need to separate the SOP bins by relatively largefrequency separation. Only the OFDM SOP will be analyzed in detailherein and it will be understood that one may exploit the other SOPchoices as needs dictate.

As depicted in FIG. 10, the exemplary SOP operates in the followingfashion. The symbols from the transmit spatial pre-processor, z_(j)(n),considered to be in the frequency domain, are organized into M_(T)vectors of N complex symbols. Each of these vectors is then converted tothe time-domain using an N-point inverse-fast-Fourier-transform (IFFT)procedure 205. Each of the parallel M_(T) time-domain sequences has acyclic prefix added to the beginning, so that the last v elements in theIFFT output sequence form a pre-amble to the N-element IFFT output. Thecyclic prefix operation is given by:[z(1) . . . z(N)]^(T)

[z(N−v+1) . . . z(N) z(1) . . . z(N)]^(T)

The application of the cyclic prefix is performed by cyclic prefixapplication procedure processor 207. For each antenna, the (N+v)-lengthsequences are passed to the RF transmit chain for D/A conversion andmodulation.

Likewise, each RF receiver chain produces a sampled sequence of lengthN+v. Cyclic prefix removal procedure processors 206 remove the cyclicprefix from each sequence by discarding the first v data symbols,resulting in M_(R) vectors of N complex symbols. Each of these M_(R)sequences is then processed with an N-point fast-Fourier-transform(FFT). These symbols are then passed to the receiver spatial processor.

The effect of the SOP is to substantially remove the ISI between any twosymbols assigned to different bins, for any pair of transmit and receiveantennas. Therefore, for each IFFT-FFT bin n, the received signal valuesfor each antenna, x(n), are related to the transmitted frequency-domainsymbols, z(n), through the expression,x(n)=H(n)z(n)+I(n)∀n  (10)

where x(n) is a complex M_(R)-element vector at SOP bin n, z(n) is acomplex M_(T)-element symbol vector at bin n, and I(n) is theinterference and noise at all receive antennas for bin n. Note that atime index is not included in the above equation since it is assumedthat channel is time-invariant over the length of a burst. The spatialsub-channels, H(n), are M_(R) by M_(T) element matrices that describethe spatial correlation remaining in the wireless channel after the SOP.For the MIMO case, each SOP bin may be characterized by a matrix ofcomplex values, with each value representing the path gain from a giventransmit antenna element to a given receive antenna element in thatparticular SOP bin.

To understand the result given by Equation(10), it is instructive toshow how the SOP pre-processor and post-processor acts upon thetime-domain channel. The MIMO time-domain channel, G(k), containsM_(R)M_(T) Toeplitz matrices that describe the time-domain input-outputbehavior of each antenna pair (see eq. 1). This channel formulation isdepicted in FIG. 10. It is well known that by adding a cyclic prefix atthe transmitter and subsequently removing the prefix at the receiver, aToeplitz input-output matrix is transformed into a circulantinput-output matrix (the ith row is equal to the jth row cycliclyshifted by i-j elements). Therefore, the each G_(i,j) in FIG. 10 istransformed into a circulant {tilde over (G)}_(i,j). The MIMO circulantmatrices are delimited in FIG. 10 by {tilde over (G)}.

This particular class of SOP exploits the fact that any circulant matrixcan be diagonalized by a predetermined matrix operator. One suchoperator is a matrix of the FFT basis vectors. That is, for anycirculant matrix {tilde over (G)},D=G{tilde over (Y)}Y^(H)

where D is some diagonal matrix and the scalar elements of Y are,$y_{m\quad n} = {\frac{1}{\sqrt{N}}{{\mathbb{e}}^{{- {j2\pi}}\quad m\quad{n/N}}.}}$

Applying M_(T) IFFT operations at the transmitter and M_(R) FFToperations at the receiver is described mathematically by apre-multiplication of a NM_(R)×NM_(R) block diagonal FFT matrix andpost-multiplication of a NM_(T)×NM_(T) IFFT matrix. For example, theformer matrix is defined, $Y_{(M_{R})} = {\begin{bmatrix}Y & \quad & 0 \\\quad & ⋰ & \quad \\0 & \quad & Y\end{bmatrix}.}$

Therefore, including the transmitter IFFT and receiver FFT operations,the input-output relationship is described by${{Y_{(M_{R})}\overset{\sim}{G}Y_{M_{T}}^{H}} = \begin{bmatrix}D_{1,1} & \cdots & D_{1,M_{T}} \\\vdots & ⋰ & \vdots \\D_{M_{R},1} & \cdots & D_{M_{R},M_{T}}\end{bmatrix}},$

where D_(i,j) is the diagonal matrix containing the SOP bin strengthsfor the antenna pair (i,j). Pre-multiplication and post-multiplicationby permutation matrices P_(T) and P_(R) represents the collection of allantenna combinations that correspond to a common frequency or SOP bin.This collection process, depicted in FIG. 10, results in a blockdiagonal matrix that relates the inputs and outputs:${{P_{R}Y_{(M_{R})}\overset{\sim}{G}Y_{M_{T}}^{H}P_{T}} = \begin{bmatrix}{H(1)} & \quad & 0 \\\quad & ⋰ & \quad \\0 & \quad & {H(N)}\end{bmatrix}},$

which is equivalent to Equation (10).

Spatial Processing

The spatial processing procedure is now considered. Since the SOPestablishes N MIMO spatial channels that are substantially independentfrom one another (Equation 10), one can consider the spatial processingwithin each bin separately. Representative application of spatialprocessing to frequency bin 1 will be considered as shown in FIG. 11 atthe transmitter and FIG. 12 at the receiver. FIG. 11 shows M symbols:z(1,1) through z(1,M). The notation z(n,m) refers to the symboltransmitted in bin n and spatial direction m. These M symbols willjointly occupy frequency bin 1. Each TSW 210A-C applies a weight vectorto the symbol appearing at its input, and the elements of the resultantvector are routed to M_(T) summing junctions 211. One may consider theTSWs as being multipliers taking each input symbol and multiplying it bya vector that corresponds to a spatial direction in M_(T)-space.Furthermore, the M vectors define a subspace in M_(T)-space. Note thatthe TSW vectors are considered to be column vectors in the discussionthat follows. When these M vectors are collected into a matrix, theresult is an input orthogonalizing matrix or beneficial weighting matrixfor that bin. For each input bin, a vector including symbols allocatedto subchannels corresponding to the bin is multiplied by the inputorthogonalizing matrix to obtain a result vector, elements of the resultvector corresponding to the various transmitter antenna elements.Together, the TSWs 210A-C make up one embodiment of a Transmit SpatialProcessor (TSP) 230.

Each RSW 220A-C accepts MR inputs, one from each receiver antenna path.Within the m^(th) RSW, a weight vector is applied to the inputs (i.e. aninner-product is performed) thereby producing a received signal samplex(1,m):${{x\left( {1,m} \right)} = {{u\left( {1,m} \right)}\begin{bmatrix}{x_{1}(1)} \\\vdots \\{x_{M_{R}}(1)}\end{bmatrix}}},$

where u(1,m) is the RSW for bin 1 and spatial direction m. Similar to aTSW, a RSW vector has an associated direction in M_(R)-space. Each RSWmay also be considered to be a multiplier. This vector is considered tobe a row vector. When these M RSW vectors are collected into a matrix,the result is an output orthogonalizing matrix or beneficial weightingmatrix for that bin. When a vector including symbols in a particularoutput bin produced by the SOP for each receiver antenna is multipliedby the output orthogonalizing matrix, the result is a vector includingsymbols received in that bin for various spatial directions. Together,the RSWs 220A-220C represent one embodiment of a Receive SpatialProcessor (RSP) 240.

Through proper choice of the weight vectors applied via the TSWs andRSWs, the M spatial directions can be made substantially orthogonal toone another. The result is that the received signal sample x(1,m)depends only upon input symbols z(1,m) and not the M−1 other inputsymbols for SOP bin 1. Methods for selecting the TSP and RSP weightvectors are described in detail below.

The spatial processing described above can be applied to the other N−1frequency bins in addition to frequency bin 1. The block diagram forsuch a system is depicted in FIG. 13 for the transmitter and FIG. 14 forthe receiver. SOP processors 190 and 200 ensure that the frequency binsremain substantially orthogonal to one another while TSP 230 and RSP 240ensure that M substantially orthogonal spatial channels exist withineach frequency bin. The net result is that NM substantially parallelsubchannels are constructed within the MIMO communication system. Inother words, the combination of SOP processors 190 and 200, TSP 230, andRSP 240 create a set of substantially independent space-frequencysubchannels,x(n,m)=H(n,m)z(n,m)+I(n,m)∀n,m.

This simultaneous substantial orthogonalization of space and frequencycan result in a significant increase in spectral efficiency sincemultiple data streams are being communicated through the channel. Notethat the number of substantially independent subchannels possible, inthe multipath case, is equal to the number of SOP bins multiplied by thenumber of transmit antennas or the number of receive antennas, whicheveris smaller. Therefore, the total number of space-frequency subchannelsis less than or equal to N min(M_(T),M_(R)), when multipath is present.

An exemplary set of TSWs and RSWs are derived from the singular valuedecomposition (SVD) of the spatial channel matrix for each bin,H(n)=U(n)Σ(n)V(n)^(H).

The input singular matrix, V(n), contains M_(T) column vectors thatdefine up to M_(T) TSWs for bin n. Likewise, the output singular matrix,U(n), contain M_(R) column vectors that when Hermitian transposed,define up to M_(R) RSW row vectors for bin n. The TSWs and RSWs forother bins are determined in the same fashion, through an SVDdecomposition of the spatial matrix for that bin. Using this spatialprocessing, substantially independent multiple streams of symbols can betransmitted and received. The strength of each subchannel is equal toone of the elements of the diagonal matrix Σ. These subchannelsstrengths will vary. Therefore, the subchannels will have varying signalto noise ratios and information capacity. For this reason, it may bepreferable to transmit and receive only on a subset of the possiblesubchannels, or M<min{M_(T),M_(R)}. For example, it may be improvidentto use processing complexity on the weakest subchannels that may have avery small information carrying capacity. In this case, spatialprocessing is used to increase the received power of one or moreparallel symbol streams. It may also be preferable to use codingtechniques to leverage strong subchannels to assist in the use of weakersubchannels. It may also be preferable to allocate either bits ortransmit power among the subchannels to maximize the amount ofinformation communicated.

The exemplary spatial processing described above requires cooperationbetween the transmitter and receiver to effectively orthogonalize thespatial channel for each bin. Alternatively, this orthogonalization canbe accomplished at only one end of the link. This can be advantageouswhen one end of the link can afford more computational complexity thanthe other end. In addition, spatial orthogonalizing at one end can beadvantageous when the channel model is known only at that end.

Consider the case where the orthogonalization is done at the receiver.Symbols are transmitted along directions defined by some set of TSWs,v(n,m). When M TSWs corresponding to the same bin are collected into amatrix V(n), the composite spatial channel is,H′(n)=H(n)V(n).

This composite channel describes the MIMO channel in bin n from theM-inputs to M_(R) outputs. The spatial processing at the receiver cansubstantially orthogonalize this composite channel, H′(n), by applyingappropriate RSWs even if the transmitter does no spatial processing. Letthese RSWs be defined as the row vectors of the weighting matrix,W_(R)(n)

Two exemplary methods for determining W_(R)(n) are referred to as thezero-forcing (ZF) solution and minimum-mean-square-error (MMSE)solution. In the ZF approach, the weighting matrix is thepseudo-(left)-inverse of the composite channel,W _(R)(n)=H′(n)^(⊥).

This results in,W _(R)(n)H′(n)=I,

where the identity matrix is M by M. Hence, the ZF solution, not onlyorthogonalizes the spatial channel for bin n, but it equalizes thestrengths of each resulting subchannel. However, the signal-to-noiseratio for the various subchannels can vary widely. One skilled in theart will recognize that the ZF solution can result in amplification ofthe interference and noise unless the composite channel, H′(n), isnearly orthogonal to begin with.

An MMSE solution, on the other hand, does not amplify noise. For theMMSE approach, the weight, W_(R)(n), satisfies,${\min\limits_{W_{R}{(n)}}{E\left\{ {{{{W_{R}(n)}{x(n)}} - {z(n)}}}^{2} \right\}}},{or},{{W_{R}(n)} = {R_{{z{(n)}}{x{(n)}}}R_{x{(n)}}^{- 1}}},$

where R_(x(n)) is the covariance matrix for x(n) and R_(z(n)x(n)) is thecross-covariance between z(n) and x(n). Using,

x(n)=H′(n)z(n)+I′(n),

and the fact that R_(z(n))=σ_(z) ²I, results in the MMSE weight,${W_{R}(n)} = {{H^{\prime}(n)}^{H}{\left( {{{H^{\prime}(n)}{H^{\prime}(n)}^{H}} + {\frac{1}{\sigma_{z}^{2}}R_{I^{\prime}}}} \right)^{- 1}.}}$

Note that when I(n) is spatially white noise, then R_(I)=σ_(I) ²I.

Similarly to the above orthogonalization at the receiver, the channelcan be orthogonalized at the transmit end only. For this to occur, thetransmitter is required to have knowledge of the RSWs to be used by thereceiver. In a TDD channel, where the channel exhibits reciprocity,these RSWs can be learned when that transceiver uses TSW directionsequal to the RSW directions. Alternatively, the receiver may not do anyspatial processing, so the transmitter is responsible for spatialorthogonalization.

In this case, the composite channel isH′(n)=U(n)H(n),

where the matrix U(n) is composed of the RSW row vectors, u(n,m). Thiscomposite channel describes the MIMO channel in bin n from M_(T) inputsto M outputs. Similar to the previous case, the transmitter cansubstantially orthogonalize this composite channel, H′(n), by applyingappropriate TSWs. These TSWs are the column vectors of the weightingmatrix, W_(T)(n).

The transmit weighting can be determined using the ZF or the MMSEapproach. In the ZF approach, the weighting matrix is equal to thepseudo-(right)-inverse of H′(n). The MMSE solution satisfies${\min\limits_{W_{T}{(n)}}{E\left\{ {{{{H^{\prime}(n)}{W_{T}(n)}{z(n)}} + {I^{\prime}(n)} - {z(n)}}}^{2} \right\}}},$

An important simplification to the general space-frequency processingtechnique is the use of only one spatial direction for each bin of theSOP. This case is depicted in FIG. 15 for the transmitter and FIG. 16for the receiver. In this case, only N subchannels are created. The Ninput symbols, z(1,1) through z(N,1), are processed by N TSWs 210A-Bthat weight and allocate these N symbols among the M_(T) identical SOPprocessors 190. At the receiver, the antenna samples are processed byM_(R) SOP processors 200. The M_(R) SOP outputs corresponding to acommon bin are weighted and combined in N RSWs 220A-B. With N suchweightings, the result is N outputs, x(1,1) through x(N,1), of the Nsubstantially orthogonal subchannels.

When only one spatial direction is used in the TSP and RSP, oneexemplary choice for the particular weightings are the TSW and RSWdirections that result in maximum subchannel strength. This maximizesthe signal-to-noise ratio (SNR) of the received signals, x(1,1) throughx(N,1). In this case, the optimal weightings should satisfy,${\max\limits_{{u{(n)}},{v{(n)}}}{{{u(n)}{H(n)}{v(n)}}}^{2}},$

with the implicit constraint on the size (2-norm) of both the RSW weightu(n) and the TSW weight v(n). To determine the solution to thisoptimization problem, consider the SOP outputs for bin n when a singleTSW, v(n,1), is used, $\begin{bmatrix}{x_{1}(n)} \\\vdots \\{x_{M_{R}}(n)}\end{bmatrix} = {{{H(n)}{v\left( {n,1} \right)}{z\left( {n,1} \right)}} = {{h(n)}{{z\left( {n,1} \right)}.}}}$

The quantity h(n) is referred to as the received channel vector. Achannel identification technique is used to determine the receivedchannel vector. Therefore, the optimal RSW weight is equal to theHermitian of the received channel vector, h(n),u(n)=h(n)^(H).

Note that this is true regardless of the particular value of v(n). Theoptimal TSW direction, on the other hand, satisfies,${{\max\limits_{v{(n)}}{{u(n)}{H(n)}{v(n)}}} = {\max\limits_{v{(n)}}{{v(n)}^{H}{H(n)}^{H}{H(n)}{v(n)}}}},$

where the optimal RSW direction has been used. The optimal TSW for bin nis equal to the scaled maximum eigenvector of the matrix H(n)^(H)H(n).One skilled in the art will recognize that the optimal RSW is also equalto the scaled maximum eigenvector of H(n)H(n)^(H).

A further advantageous simplification of the above techniques is the useof one or more common TSW and RSW directions for all bins. In otherwords, every bin has the same TSW and RSW weights. These weight vectorsmay also consider delay elements. In one embodiment, these weights aredetermined to maximize the SNR of the received signals, averaged overfrequency n. This is depicted in FIG. 17 for the transmitter and FIG. 18for the receiver. Consider this embodiment with one spatial direction.In this case, the TSW and RSW weights satisfy, $\begin{matrix}{{\max\limits_{u,v}{E_{n}\left\lbrack {u\quad{H(n)}v} \right\rbrack}^{2}},} & 50\end{matrix}$

Note that the expectation operator, E_(n), represents averaging over SOPbins. This averaging could also be done over multiple bursts in additionto frequency. The solution to this problem is when v is equal to themaximum eigenvector ofR _(d) =E _(n) {H ^(H)(n)H(n)},  51

and u is equal to the maximum eigenvector of the covariance matrixformed from averaging the outer product of the receive vector channel,R _(h) =E _(n) {h(n)h(n)^(H)}.  52

The quantity R_(d) is the spatial covariance matrix that describespreferable directions to transmit to the desired receiver, a desiredsubspace.

This technique can be generalized to the case where multiple directionsare utilized. In this case, M TSWs and M RSWs are determined to maximizethe average (over bin) SNR received through the M spatial directions.The M spatial directions will not necessarily be orthogonal to eachother. Therefore, there will be spatial crosstalk in the receivedsymbols. Multidimensional encoding and decoding techniques discussedbelow can then achieve a multiplicative rate increase in the presence ofsuch crosstalk.

Alternatively, the receiver can spatially orthogonalize the subchannelsby further weighting of the M outputs from the RSWs. The compositespatial channel at bin n, with the RSWs and TSWs included isH′(n)=UH(n)V,  53

where the matrix U is made up rows equal to the RSW directions and V isa matrix with columns equal to the TSW directions. Since U and V weredetermined based on an average SNR criterion for all bins, the compositematrix H′(n) will not be diagonal. Hence, the receiver can apply theadditional weight, W_(R)(n), to orthogonalize H′(n). Alternatively, thetransmitter can use the additional weight, W_(T)(n), to spatialorthogonalize the composite channel. Exemplary solutions for theseweightings are the joint SVD, the ZF and MMSE. The advantage of thisapproach is that the processing required to adapt all N SOP bin matrixchannels may be substantially higher than the processing complexity toadapt the average TSP and RSP.

The rejection and prevention of interference can be accomplished inconjunction with the space-frequency processing discussed above. This isespecially useful when the number of spatial directions used forcommunication is less than the number of antennas. This case occurs whenweak spatial directions are not utilized or when the number of antennasat the receiver and transmitter are not the same. In either case, one orboth ends of the communication link have extra spatial degrees offreedom to use for the purpose of mitigating interference.

The amount of interference arriving at an antenna array can bequantified by the interference covariance matrix,R _(I)(n)=E{I(n)I(n)^(H)},

where I(n) is the M_(R) length interference plus noise vector receivedin SOP bin n. This matrix defines an undesired interference plus noisesubspace in M_(R)-space for bin n. The interference plus noise energythat contaminates a particular received subchannel symbol with bin n andspatial direction m, is equal to,u^(H)(n,m)R_(I)(n)u(n,m),

where u(n,m) is the combining weight vector for the RSP(n,m). Anadvantageous interference rejection technique is then to “whiten” theeffect of the interference across the spatial directions, so that theinterference is minimized and spread evenly across all spatialdirections used. Therefore, each of the RSP weighting vectors aremodified by the matrix R_(I) ^(−1/2)(n),u′(n,m)=u(n,m)R _(I) ^(−1/2)(n).

Alternatively, the RSP weighting vectors are the vectors of the outputsingular matrix, U′(n), from the SVD of the modified spatial channel,R _(I) ^(−1/2)(n)H(n)=U′(n)Σ′(n)V′(n)^(H).

Note that a very useful simplification of the above interferencerejection technique is to average the interference covariance matrixover all N bins and possibly a set of bursts to arrive at an averagespatial interference covariance matrix, R_(I), that is independent ofbin n. In this case, every RSP combining vector is modified in the sameway due to interference. This approach can significantly reduce theamount of computations needed to determine R_(I) and R_(I) ^(−1/2). Notethat it is often beneficial to add a scaled matrix identity term toestimates of the interference covariance matrix to reduce thesensitivity of these interference mitigation approaches to covarianceestimation errors.

Similar interference mitigation techniques can be advantageouslyemployed at the transmitter to reduce the amount of interferenceradiated to unintentional receivers. In the TDD channel, reciprocity inthe radio link allows the undesired receive interference subspace ineach SOP bin to be accurately used to describe the transmitter subspace.That is, the amount of interference transmitted to unintentionalreceivers isV^(H)(n,m)R_(I)(n)v(n,m),  60

where v(n,m) is the transmit weight vector for the TSW(n,m). An optimalinterference reduction approach is then to minimize and “whiten” thetransmitted interference across spatial directions. In the same fashionas the receiver case, the TSW vectors are modified by the matrix R_(I)^(−1/2)(n). Alternatively, the TSP weight vectors are the vectors of theinput singular matrix V′(n) from the SVD of the modified spatialchannel,H(n)R _(I) ^(−1/2)(n)=U′(n)Σ′(n)V′(n)^(H).  61

Again, a significant simplification occurs when the interferencecovariance matrix is determined by averaging over frequency or SOP bins.It is especially advantageous to average over SOP bins in afrequency-division-duplex (FDD) system, where significant averaging ofthe receive covariance matrix results in a good estimate of the transmitcovariance, even though instantaneous channel reciprocity does not hold.

Interference rejection at the receiver and interference reduction at thetransmitter are done together by simply combining the two techniquesoutlined above. In this case, the RSP vectors and TSP vectors arecontained in the input and output matrices of the SVD of,R_(I,R) ^(−1/2)(n)H(n)R_(I,T) ^(−1/2)(n).

As outlined previously, it can be advantageous to use the same TSWs andRSWs for all bins. This approach can be combined with interferencemitigation by the determining the transmit and receive weight vectorsthat maximize average power delivered to the receiver of interest, whileat the same time, minimizing power delivered to other undesiredreceivers. There are various optimization problems that can be posed todetermine these TSP or RSP directions, each involving the desiredreceiver covariance matrix and the undesired covariance matrix. Forexample, one TSP problem is${\max\limits_{v}{v^{H}R_{d}v\quad{such}\quad{that}\quad v^{H}T_{I}v}} \leq {P_{I}\quad{and}\quad v^{H}v} \leq {P_{T}.}$

That is, a TSP direction is chosen for all SOP bins that transmits themaximum amount of power to the desired receiver while maintaining atransmit power limit, P_(T), and a transmitted interference limit,P_(I). For this particular problem, the TSP direction is equal to themaximum generalized eigenvector of the matrix pair {R_(d),(R_(I)/P_(I)+I/P_(T))}. One example of an effective interference rejecting RSP for allSOP bins is a weighing that maximizes the average received SINR. The RSPthat maximizes SINR is the maximum eigenvector of the matrix R_(I)^(−1/2)R_(d)R_(I) ^(−1/2).

One further simplification to the above algorithm is to model theinterference and/or the desired covariance as diagonal, or nearlydiagonal. When both R_(d) and R_(I) are diagonal, the solution to theabove optimization problem reduces to the maximal ratio SINR combiner,u, and transmitter, v. It is also sometimes preferable to only considerother subsets of the elements of either the desired or interferencecovariance matrices.

One skilled in the art will also recognize that all the TSPs and RSPscan be used when there is only one SOP bin, such as a common frequency.

Space Frequency Coding

Many of the advantageous space frequency encoding techniques embodied inthe invention may be broadly classified in two exemplary categories. Thefirst category involves techniques wherein the spatial matrix channelwithin each SOP bin undergoes space frequency processing at thetransmitter, or the receiver or both, resulting in a substantiallyindependent set of one or more parallel communication subchannels withineach SOP bin. The objective of the encoder and decoder in this case isto appropriately allocate the transmitted information among multipleindependent space-frequency subchannels using interleaving, power andbit loading, or both. The second category of space frequency encodinginvolves transmitting and receiving one or more symbol sequences in eachSOP bin using one or more transmitter and receiver weight vectorcombinations that are not necessarily intended to create independentspatial subchannels within each SOP bin. This results in significantcross-talk between each symbol stream present at the receiver output. Adecoder then uses knowledge of the equivalent matrix channel within eachSOP bin, and knowledge of the set of possible encoder sequences toestimate the encoder symbol sequence that gave rise to the cross-talkrich output SOP bin vector sequence. The main differentiating featurebetween the first approach and the second approach is the presence orlack of spatial processing that results in substantially orthogonalspatial subchannels within each SOP bin. Both approaches have theadvantageous ability to multiply the data rate that can be achieved inMIMO channels with multipath.

Coding for Substantially Orthogonal Space-Frequency Subchannels

In applications where the spatial channels are processed to achievemultiple substantially independent spatial subchannels within each SOPbin, an advantageous embodiment of the invention involves encoding theinput data sequence into a digital symbol stream that is then routed invarious beneficial ways through the available parallel space frequencysubchannels. FIG. 22 depicts a preferred embodiment. This embodimentinvolves distributing the symbol outputs of a single encoder among allof the available space frequency subchannels. Several known codingschemes that can be combined effectively with space frequency processingto distribute information transmission over the space and frequencydimensions of a communication channel. This discussion assumesestimation of the MIMO channel by transmitting a series of trainingsymbol sequences from each antenna element as discussed herein. Thediscussion further assumes that the receiver and transmitter eithershare the information required to decompose the channel into parallelsub-channels, or the TDD techniques discussed herein are used to do thesame.

Referring again to FIG. 22, the preferred embodiment exploits a threelayer coding system. The first layer of coding includes the combinationof transmitter TSWs 210A through 210B, Transmitter SOP processors 190,receiver SOP processors 200, and receiver RSWs 220A through 220B. Thisfirst layer of coding performs the spatial processing. The second layerof coding includes a Trellis Encoder and Interleaver (420) at thetransmitter in combination with a Deinterleaver and ML Detector 430 atthe receiver. The third layer code involves Reed Solomon (RS) Encoder410 at the transmitter in combination with an RS Decoder 440 at thereceiver. The bit level RS coding occurs prior to the trellis encodingand the Reed Solomon codeword detector acts upon the bit sequence fromthe ML detector. The fourth layer of coding involves an ARQ code thatrecognizes Reed Solomon codeword errors at the receiver in the ReceiverARQ Buffer Control 450 and requests a codeword retransmission from theTransmitter ARQ Buffer Control 400. The retransmission request is madethrough a Reverse Link Control Channel 460. The reverse control channelis a well known radio system concept and will not be discussed herein.This combination of coding techniques and space frequency processing ispreferable because it provides for a rich combination of space andfrequency diversity and it is capable of obtaining very low bit errorrates. The detailed operation of the RS encoder and decoder, as well asthe ARQ system is well known to one skilled in the art. Following thisdiscussion, it will be clear to one skilled in the art that othercombinations of one or more of these four coding elements may beemployed with advantageous results in various applications.

The trellis coding step may be substituted with CBM-QAM or a turbo code.Similarly, the Reed-Solomon code may be substituted with a block code,or with an error checking code such as a CRC code. The transmitter endwould then include the necessary encoder and the receiver end wouldinclude the necessary decoder.

There are at least two basic methods for employing trellis coding todistribute information among substantially independent space frequencysubchannels. One method is adaptive encoding that modifies the bit andpower loading for each subchannel according to its quality. The secondmethod involves maintaining constant power and bit loading for all spacefrequency subchannels. Both of these methods are discussed below.

Space Frequency Trellis Coding with Orthogonal Spatial Subchannels andAdaptive Power and Bit Loading

FIG. 22 depicts the coding and interleaving detail for the transmitterand receiver portions of the present embodiment. Encoding andInterleaving system 10 encodes the data into a set of complex symbols.Each of the complex symbols is then allocated to a particulartransmitter TSW (210A through 210B). The input to each TSW forms avector of frequency domain symbols that are fed into the same bin of oneor more transmit SOP processors. Each transmitter TSW, possibly inconjunction with a receiver RSW converts the matrix channel within eachSOP bin into a set of substantially orthogonal space frequencysubchannels using one of the methods discussed herein.

FIG. 23 displays a more detailed diagram of the encoder and interleaver.An Information Allocation Unit 360 assigns the bits and the transmitterpower that will be allocated to each space frequency subchannel. Onemethod for accomplishing this assignment is the so-called gap analysis.In this technique, a particular coset code with an associated latticestructure is characterized by first determining the SNR required toachieve a theoretical capacity equal to the desired data rate. The codegap is then the SNR multiplier required to achieve the targetprobability of error at the desired data rate. In a parallel channelcommunication system, this gap can be used to determine the power andbit distributions that maximize data rate subject to a probability oferror constraint. With a coding gap of α, the rate maximizingwater-filling solution for the space frequency subchannels becomes${{p\left( {n,m} \right)} = \left( {\xi - \frac{\sigma_{n}^{2}\alpha}{{{\lambda\left( {n,m} \right)}}^{2}}} \right)^{+}},$

where σ_(n) ² is the noise power and m is the spatial index and n is theDFT frequency index. The bit allocation per sub-channel is then given by${b\left( {n,m} \right)} = {{\log\left( {1 + \frac{{p\left( {n,m} \right)} \cdot {{\lambda\left( {n,m} \right)}}^{2}}{{\alpha\sigma}_{n}^{2}}} \right)}.}$

After the power and bit loading assignments are accomplished in theInformation Allocation Unit, the bits are encoded with a Trellis Encoder370. It is not possible to achieve infinite bit resolution (granularity)with coset codes. Therefore the gap analysis solution should bemodified. Several bit loading algorithms exist to resolve this problem.One method involves rounding down the water filling solution to thenearest available quantization. The granularity of possible bitallocations is determined by the dimensionality of the coset codelattice structure. In the MIMO channel communication structuresdescribed herein, the orthogonal constellation dimensions are thecomplex plane, space, and frequency.

FIG. 26 illustrates an example of a practical method for bit loadingwith a trellis encoder that uses a one dimensional QAM symbolconstellation. The bit load is adjusted down for a given trellis encoderoutput symbol by assigning a number of fixed zeros to one or more of theinput bits to the encoder. FIG. 26 shows the operation of the trellisencoder and the trellis state diagram for the decoder for foursuccessive symbol transmissions. Four bits are assigned to the firstspace frequency subchannel. A first subchannel trellis encoder input 350is assigned 4 bits so Symbol 1 can take on any one of 32 values. Thereare two bits feeding the convolutional encoder, and two bits feeding thecoset select. The ML detector at the receiver uses the trellis statediagram and the channel state information to solve the maximumlikelihood recursion. This is efficiently accomplished with the Viterbialgorithm. The trellis code state diagram defines a set of symbolsequence possibilities {Z}. The space frequency subchannel is denotedĤ(n,k), for SOP bin n at burst k. The maximum likelihood equation isthen given by$\left\{ {{\hat{z}(1)}^{T},{\hat{z}(2)}^{T},\cdots\quad,{\hat{z}(N)}^{T}} \right\} = {\arg\left\{ {\min\limits_{\{{{\hat{z}{(1)}}^{T},{\hat{z}{(2)}}^{T},\cdots\quad,{\hat{z}{(N)}}^{T}}\}}{\sum\limits_{n = 1}^{N}{{{{\hat{H}\left( {n,k} \right)}{z(n)}} - {x\left( {n,k} \right)}}}^{2}}} \right\}}$

where z(n) is the symbol hypothesized for SOP bin n. The decoder outputstate diagram for first space frequency subchannel 340 includes fourpossible parallel transitions for each trellis branch and all of thetrellis branches are possible. The second space frequency subchannel inthe sequence is assigned three bits so a second trellis encoder input352 shows one bit fed into the coset select with two bits still feedingthe convolutional encoder. A decoder state diagram 342 for the secondspace frequency subchannel has only two parallel transitions for eachtrellis branch but still maintains all trellis branch possibilities.Continuing in succession, a third space frequency subchannel is assignedonly two bits to an encoder input 354 so there are no paralleltransitions considered by a trellis decoder state diagram 344. In afourth space frequency subchannel, only one bit is assigned to anencoder input 356 so there are no parallel transitions and some of thetrellis state branches (346) are no longer considered by the decoder. Itis understood that FIG. 26 is provided as a graphical aid and is notintended to represent an actual design.

The maximum Euclidean distance error sequence design metric is onepreferable choice for a trellis encoder used with the parallel spacefrequency channel with this bit and power loading embodiment of theinvention. Other code error sequence design metrics that areadvantageous in various application conditions include product distanceand periodic product distance.

Referring again to FIG. 23, the output of the encoder is interleavedacross the various space frequency subchannels using Interleaving block260. Typically, the interleaving process distributes the symbols so thatsymbols that are near one another at the encoder output are wellseparated in both the SOP bin assignment and the spatial subchannelassignment. This distributes the effects of channel estimation errorsand localized frequency domain or spatial domain interference so thatthe decoder error is reduced. It is understood that the bit and powerassignments by Information Allocation block 360 take place withknowledge of the post-interleaved channel strength. It is understoodthat the encoding and decoding process can begin and end within oneburst, or it may take place over a multitude of bursts.

One skilled in the art will recognize that a multitude of lesssophisticated adaptive power and bit loading algorithms can beadvantageously applied to a substantially independent set of spacefrequency subchannels. One example is an algorithm wherein a spacefrequency subchannel is either loaded with maximum power or no power andthe bit distribution may be adjusted in only two increments.

A second alternative embodiment shown in FIG. 19 includes one encoderfor each SOP bin, with the output symbols of each encoder allocatedamong several spatial subchannels. A third embodiment shown in FIG. 20involves one encoder for each spatial subchannel, with the outputsymbols of each encoder distributed among the SOP bins for that spatialsubchannel. A fourth embodiment shown in FIG. 21 involves a separateencoder for each available space frequency subchannel.

It will be clear to one skilled in the art that the channel estimationtools taught herein are very useful in improving the accuracy of thechannel estimates used for the bit loading and decoding process.

One skilled in the art will recognize that many of the other codingtechniques for parallel sub-channel bit loading communication systems,not mentioned here, can also be applied to the present invention.

Space Frequency Trellis Coding with Orthogonal Spatial Subchannels andFlat Power and Bit Distribution

In some cases it is difficult to adaptively load the power and bitassignments for each available space frequency subchannel. For example,the transmitter and receiver may not be able to adapt the loading fastenough to accommodate time domain variation in the channel. In anotherexample, the required feedback from the receiver to the transmitterrequires a significant portion of the available reverse link bit rate.Adaptive bit loading may also be overly complicated for certainapplications. Thus, it is often advantageous to encode and decode asymbol stream in such a manner that the power and bit allocation isconstant for all space frequency subchannels. This is easilyaccomplished by employing the embodiments depicted in FIGS. 22-23, andassigning a constant power and bit allocation to all space frequencysubchannels in the Information Allocation block 360.

Space Frequency Coding without Orthogonal Spatial Subchannels

In applications where the spatial channels are not processed to achievesubstantially orthogonal spatial subchannels within each SOP bin, anadvantageous embodiment of the invention involves utilization of avector maximum likelihood decoder in the receiver to decode a symbolsequence that includes multiple symbols per SOP bin. The vector maximumlikelihood detector is capable of determining the transmitted symbolvector in each SOP bin even in the presence of spatial subchannels thatcontain significant cross-coupling between the channels. The vectormaximum likelihood detector uses an estimate of the matrix channel fromeach SOP bin to decode a sequence of groups of symbols with one groupfor each SOP bin. The groupings will be referred to here as amultidimensional symbol vector, or simply a symbol vector. The MLdetector uses an estimate of the matrix channel that exists in each SOPbin to find the most likely sequence of transmitted encoder vectorsymbols.

FIG. 24 depicts a transmitter system wherein multiple space/frequencysubchannels are employed without spatial orthogonalization. FIG. 25depicts a receiver system for this application.

The bit sequence b(k) is encoded into a sequence of multidimensionalsymbol vectors in a Bit to Symbol Encoding block 250. Each output of theencoder is an M₀ by 1 complex symbol vector, where M₀ is the number ofspatial directions that will be used for transmission. Note that M₀ ispreferably chosen to be less than or equal to M_(T). A preferableconstruction of the encoder is a multidimensional trellis encoder. Oneadvantageous metric for designing the trellis encoder constellation andconvolutional encoder polynomial will be provided below. Within thepreviously discussed Symbol Interleaver block 260, the vector symbolsequence is demultiplexed and interleaved with a Symbol SequenceDemultiplexor 300 and a Transmit Symbol Routing block 310. TransmitSymbol Routing block 310 interleaves the vector symbol sequence so thatthe elements of a given vector symbol are grouped together andtransmitted in one SOP bin. Thus, different vectors are separated by amultitude of SOP bins before transmission, but all elements within thevector symbol share the same SOP bin. The purpose of the interleaver isto distribute the vector symbol sequence so that the fading present inthe matrix channels within the SOP bins is randomized at the output ofthe receiver interleaver. The decoder can recover information associatedwith symbols that are transmitted through SOP bins that experience adeep fade, provided that the adjacent symbols do not also experience thesame fade. Since there is often a high degree of correlation in thefading experienced by adjacent SOP bins, the interleaver makes thefading more random and improves decoder error performance. Afterinterleaving, each element of a vector symbol is assigned to one antennafor the SOP bin assigned to that vector symbol. Transmitter SOPprocessors 190 perform the transmitter portion of the SOP.

After the transmitter SOP, it is often advantageous to perform spatialprocessing with TSP 230. It is understood that the matrix representingthe operation of TSP 230, i.e., the Transmitter Weight Matrix, may alsobe an identity matrix so that no weighting is implemented. It can bebeneficial to choose a number of spatial directions that is less thanthe number of transmitter antennas. In this case, the Transmitter WeightMatrix increases the dimensionality of the time domain vector sequencefrom the SOP bank. As an example of when it is advantageous to choose asubset of the available transmitter spatial directions, if the receiverhas fewer antennas than the transmitter, then it is known that theinformation capacity of the matrix channels within each SOP bin will notsupport a number of parallel information subchannels that is greaterthan the number of receive antennas. This implies that the number ofsymbols in each transmitted symbol vector, and hence the number oftransmitted spatial directions, should not be greater than the number ofreceiver antennas. As another example, in a Rayleigh fading channel, thesmallest singular values of an M_(R) by M_(T) matrix channel are onaverage much weaker than the largest singular value. This implies thatthe average information capacity contained in the smallest singularvalue may not justify the extra signal processing complexity required totransmit over that dimension. In both of these cases, it is advisable tochoose an advantageous subset of the available transmit spatialdirections.

The transmitter may not have knowledge of the individual channelmatrices within each SOP bin but may have knowledge of the covariancestatistics of the channel matrices, averaged over frequency, or time, orboth. In such cases, the Transmitter Weight Matrix can be optimized toselect one or more spatial directions that maximize the average receivedpower for the chosen number of spatial directions. The procedure foroptimizing the Transmitter Weight Matrix for this criteria is defined byEquations 50 to 52 and the associated discussion. This is one preferredmethod of selecting an advantageous set of spatial directions for theTransmitter Weight Matrix. Another advantageous criteria for selectingthe transmitter spatial directions is to maximize average received powersubject to constraints on the average interference power radiated tounintentional receivers. The procedure for optimizing the TransmitterWeight matrix for this criterion is defined by Equations 60 and 61 andthe associated discussion.

After the time domain signal is spatially processed, the signal isupconverted to the RF carrier frequency using Modulation and RF System40 before being radiated by Transmit Antennas 51. Referring now to FIG.25, at the receiver the signal is downconverted and digitized by ReceiveAntennas 111 and Demodulation and RF System blocks 120. The RSP 240 maythen be used to process the time domain signal. The operation of RSP 240may be characterized by a Receiver Weight Matrix which may be anidentity matrix. One embodiment involves optimizing the RSP weights toreduce the number of received signals from M_(R) to M₀, which is thenumber of elements in the transmitted symbol vector and is also thenumber of transmitted spatial directions. In this case, the ReceiverWeight Matrix can be optimized to increase the average signal power ineach received spatial direction. The optimization procedure toaccomplish this is defined by Equations 50 to 53 and the associatedtext.

Channel ID block 130 is used to estimate the matrix channel in each SOPbin. Procedures for channel estimation are described below. Channelstate information for each SOP bin is fed into a Symbol to Bit Detector280 which decodes the symbol sequence after it is passed through aSymbol Deinterleaver 270.

At the receiver, after de-interleaving the SOP bins, the space-frequencysequence is again converted into a serial symbol stream by Demultiplexor300. For a given set of spatio-temporal vector symbol sequencepossibilities {Z}, and an estimate, Ĥ(n,k), of the channel matrix ineach SOP bin n at burst k, the maximum likelihood detector is given byequation (70):$\left\{ {{\hat{z}(1)}^{T},{\hat{z}(2)}^{T},\cdots\quad,{\hat{z}(N)}^{T}} \right\} = {\arg\left\{ {\min\limits_{\{{{\hat{z}{(1)}}^{T},{\hat{z}{(2)}}^{T},\cdots\quad,{\hat{z}{(N)}}^{T}}\}}{\sum\limits_{n = 1}^{N}{{{R_{I}\left( {n,k} \right)}^{{- 1}/2}\left( {{{\hat{H}\left( {n,k} \right)}{z(n)}} - {x\left( {n,k} \right)}} \right)}}_{2}^{2}}} \right\}}$

where z(n) is the vector representing the code segment hypothesized forSOP bin n, and R_(I)(n,k) is the estimated noise plus interferencecovariance matrix for SOP bin n and time k. This equation can be solvedefficiently using a vector ML detector. The SOP bin channel matrixestimates are understood to include the effects of the TransmitterWeight Matrix and the Receiver Weight Matrix. It is understood that thenoise pre-whitening step in the ML detector cost function can besubstituted by a bank of RSPs that perform the interference whitening asdescribed herein.

In a Rayleigh fading channel, a desirable metric for designing thetrellis code is given by the product of a sum involving the two-norm ofvector segments of the trellis code error sequence:$\prod\limits_{n = 1}^{q}{{{\mathbb{e}}(n)}}_{2}^{2}$

where q is the number of SOP bins in the error sequence, and e(n) is thevector difference between the true multi-dimensional code symbol segmentand the incorrect multi-dimensional symbol code segment for SOP bin n.This code design metric is a generalization on the conventional productdistance metric which contains a scalar error entry in the productequation while the new code design metric contains a vector two normentry in the product equation. It should now be evident that themultidimensional encoder can be realized by either directly producing avector consisting of a multidimensional QAM symbol with the encoderoutput or by grouping complex QAM symbols from a one dimensional encoderoutput into a vector. The vector symbol encoder alternative is preferredin some cases because this approach provides for a larger metric searchresult and hence a better fading code. After deinterleaving, the decoderthat is used at the receiver searches over all possible multidimensionalsymbols within each SOP bin to maximize Equation 70. It is understoodthat one skilled in the art will recognize after this discussion thatother desirable metrics such as Euclidean distance metrics, metricsdesigned for Rician fading channels, periodic product distance metrics,and others are straightforward to construct and space-frequency codescan then be determined through well known exhaustive search techniques.

In either the one dimensional encoder case, or the multidimensionalencoder case, the encoder constellation selection and code polynomialsearch to maximize the metric can be carried out using a number of wellknown procedures.

It is possible to improve the performance of the space-frequency codingsystem described above by using a number of transmitter antennas, or anumber of receiver antennas, that is greater than the number of symbolstransmitted in each SOP bin. If the number of receiver antennas isgreater than the number of symbols in each SOP bin, then simply applyingthe approach described above is advantageous. If the number oftransmitter antennas is greater than the number of symbols transmittedin each SOP bin, then the techniques embodied in Equation 70 areadvantageous.

Channel Identification

The operation of Channel Identification block and Training SymbolInjection block 20 will now be described. The transceiver shoulddetermine the MIMO channel in order to form the TSWs and RSWs. Forcoherent spatial processing and detection, the receiver should obtain anestimate of the channel. We wish to identify the set of matrix channelsthat results after processing by the transmitter and receiver portionsof an SOP. The notation for this channel is H(n) ∀ n where n is the SOPbin index. Channel identification techniques embodied herein can beapplied to several preferable SOP pairs including the IFFT-FFT withcyclic prefix, the multiband filter bank, or any other of a number ofwell-known SOPs. The following exemplary channel identification approachexploits the correlated frequency fading across and possibly thecorrelated time fading in the channel. The correlation in the frequencydomain arises due to the limited time delay spread of the multipathchannel. The correlation in time is due to the fact that the channel,while time-varying, is driven by band-limited Doppler frequenciescreated by objects, which can include the transmitter and/or receiver,moving in the physical environment.

The wireless link is bidirectional, therefore each end of the linkshould estimate not only a receive channel, but also a transmit channel.For example, a base station should estimate both an uplink and downlinkchannel. In systems which employ time division duplexing (TDD),electromagnetic reciprocity implies the receive and transmit propagationenvironments are the same, allowing the transmit channel to be estimatedfrom the receive channel. However, the transmit and receive electronicresponses are not necessarily reciprocal, and because the net channelresponse includes the electronics, a calibration procedure should beused to account for these differences. This calibration procedureprovides for matching in the amplitude and phase response between themultiple transmitter and receiver frequency converters. Several TDDcalibration procedures are known in the prior art and will not bediscussed herein.

In systems employing frequency division duplexing (FDD), the propagationmedium is not reciprocal; however, the paths' angles and averagestrengths are the same for transmit and receive. This enables the use ofsubspace reciprocity, but incurs a more rigorous calibrationrequirement. The FDD calibration should insure subspace reciprocitywhich requires that the array response vector at a given angle onreceive is proportional to the corresponding vector on transmit. Thisrequirement is satisfied by again calibrating the amplitude and phasedifferences among the multiple transmit and receive frequency converterchannels and by matching the transmit and receive antenna elementresponse as well as the array geometry.

An alternative approach to transmit channel estimation in FDD systemsuses feedback. The transmit channel is measured by sending trainingsymbols to the receiver, which records the amplitude induced by thetraining symbols. Using receiver to transmitter feedback on a separatefeedback control channel, the training responses are sent back to thetransmitter. The transmitter, knowing the training excitations it usedand the corresponding responses through feedback, the forward channelcan be estimated.

In general, channel identification can be done either with or withouttraining. A desirable channel identification algorithm should be robustto and operate in a variety of modem implementations. A preferable MIMOchannel identification technique operates with embedded traininginserted into the data stream by Training Symbol Injection block 20 ineach burst. In this case, both data symbols and training symbols may betransmitted within a single burst. Furthermore, the channel can bedetermined in one burst, or filtering training data gathered overmultiple bursts. Being able to update the channel estimates after everyreceived burst makes the overall communication system robust to timevariation in the channel. In addition, frequent channel estimates reducethe destructive effects of imperfect carrier frequency recovery. Sinceimperfect carrier recovery imparts a phase shift to the channel thatcontinues to grow with time, shortening the time between channelestimation events keeps the channel estimation information from becoming“stale”. Note, however, any of the well known blind channel estimationtechniques can be used to determine the training symbol outputs as analternative to using training. However, adaptive blind training is moreprone to generating burst errors.

The parameters to be identified are the N MIMO spatial channel matrices.Hence, there are N·M_(R)·M_(T) complex elements to be determined,H_(I,j)(n), ∀n ∈[1,N], ∀i ∈[1,M_(R)], ∀j ∈[1,M_(T)].

By exploiting whatever correlation exists across the SOP bins, it may bepossible to reduce the amount of overhead required to identify thechannel. The amount of correlation that exists across SOP bins isdetermined by the specific implementation of the SOP. If the SOPimplementation includes the IFFT-FFT pair, and the length of the FIRchannel is time limited with v<<N, then a relatively large degree ofcorrelation exists across the SOP bins.

In certain embodiments of the invention, the desired technique shouldidentify the MIMO channel on a burst-by-burst basis, such as those withrapidly time-varying channels. This implies that training data should beincluded in every burst. If the throughput of information is to bemaximized, the amount of training data in each burst should beminimized. It is therefore useful to determine the minimum amount oftraining data required, per burst, that allows full characterization ofthe channel by the receiver. It turns out that the minimum number oftraining symbols required to sufficiently excite the MIMO channel forestimation with an OFDM SOP is M_(T)v. To understand this result,consider the identification of a SISO channel, where each of the Nvalues of the vector H_(i,j) should be found. These N values are notindependent since, ${H_{i,j} = {{Y\begin{bmatrix}h \\0\end{bmatrix}} = {X \otimes^{- 1}Z}}},$

where X is a vector of all SOP bin outputs for antenna i, Z is a vectorof bin inputs for antenna j, and h is a vector of the time-domain FIRchannel from antenna j to antenna i. The matrix operator {circle around(X)}⁻¹ represents element by element divide. Since the time-domainchannel is time limited to v samples, only v values of the transmittedsymbols, Z, need to be training values. Furthermore, the identificationof the SIMO channel only requires the same set of v transmitted trainingtones, since each SISO component in the SIMO channel is excited by thesame input data. In a system embodiment with multiple inputs (M_(T)>1),identification of the MIMO channel requires the identification of M_(T)separate SIMO channels. Hence, only M_(T)v training symbols are neededto sufficiently excite the MIMO channel for channel identification.

MIMO Identification

The identification of the MIMO channel is accomplished by separatelyexciting each of the transmit antennas that will be used forcommunication. This decomposes the MIMO identification problem intoM_(T) SIMO identification problems. In order to accomplish channelidentification in a single burst, M_(T) mutually exclusive sets of vbins are selected from the N available bins to carry training symbols.Each transmitter antenna carries training symbols in a unique one of theM_(T) sets of bins, while transmitting no energy in the bins containedin the union of the remaining M_(T)−1 sets of v bins. This isaccomplished by choosing the TSWs 210A-C that correspond to trainingbins such that a single entry in the vector is “1” and the remainingentries equal to “0”. It is the j^(th) entry of a TSW that is set equalto “1” for those training symbols which are to be transmitted from thej^(th) antenna. For example, say that symbol bin n=2 is one of thetraining bins associated with transmit antenna 3. Then,TSW(2,1)=[0 0 0 1 . . . 0]^(T), and TSW(2,m)=0 for ∀m≠1,

and the corresponding training symbol z(2,1). By examining the contentsof each set of training bins separately, the MIMO channel response isdetermined by finding M_(T) independent SIMO channel responses.

In embodiments in which rapid updates of the channel estimate is notrequired, another exemplary training scheme may be employed. Thistraining scheme involves using just one set of v training bins. On agiven burst, one of the transmit antennas sends training symbols in thetraining bins and the other antennas transmit no energy in those bins.This allows the receiver to identify one of the M_(T) SIMO channels. Onthe next burst, a different antenna sends training symbols in thetraining bins while the other antennas transmit no energy in those samebins. The receiver is then able to identify another set of N SIMOchannels. This procedure is repeated until training data has been sentby each of the transmit antennas, allowing the entire MIMO channel to beidentified. The entire procedure is repeated continuously so that fullchannel is determined every M_(T) bursts.

SIMO Channel Identification

We have just shown that identification of the MIMO channel can beaccomplished by successive identification of each SIMO channel. It istherefore useful to discuss specific techniques for obtaining a SIMOchannel response. The following discussion assumes that the SOP is theIFFT-FFT pair. Channel identification techniques for other SOPs thatexploit frequency and possibly time correlation in the similar fashionwill be obvious to one skilled in the art.

It is assumed that a certain subset of available SOP bins are allocatedfor training. Let J be this set of frequency bins used for learning aSIMO channel. To begin, assume that J contains v bin indices.Furthermore, let Z_(t) be the v training symbols and X_(t,i) be thereceived data in the training frequency-bins from antenna i. Let thequantities ĥ_(i), Ĥ_(i) be the estimated time-domain andfrequency-domain channels from the transmit antenna under considerationto the receive antenna i. In other words, ĥ_(i) is the v-length impulseresponse from the input under consideration to output i. Likewise, Ĥ_(i)is a vector of N frequency domain values for this channel. With thesedefinitions, it can be shown that $\begin{matrix}{{{\hat{h}}_{i} = {Y_{J,\overset{\_}{v}}^{- 1}\left( {X_{t,i} \otimes^{- 1}Z_{t}} \right)}},{and}} & (81) \\{{{\hat{H}}_{i} = {Y_{\overset{\_}{N},\overset{\_}{v}}{{\hat{h}}_{i}.{where}}}},\begin{matrix}{{\overset{\_}{\nu} = \left\{ {1,2,\ldots\quad,\nu} \right\}},} \\{{{\overset{\_}{N} = \left\{ {1,2,\ldots\quad,N} \right\}},{and}}{{Y_{PQ} = {\frac{1}{\sqrt{N}}{\mathbb{e}}^{{- {j2\pi}}\quad{{pq}/N}}}},{\forall{p \in \left\{ P \right\}}},{\forall{q \in {\left\{ Q \right\}.}}}}}\end{matrix}} & (82)\end{matrix}$

This also generalizes to any number of training tones, γ, in which casethe set J includes γ bin indices. When γ≧v, the frequency domain channelcan be determined by,Ĥ _(i) =Y _(N, v) (Y _(J, v) ^(H) Y _(J, v) )⁻¹ Y _(J, v) ^(H)(X _(t,i){circle around (x)} ⁻¹ Z _(t)).  (83)

Note that many of the above calculations can be performed in advance ifthe training bins are predetermined and fixed. Then, the matrix Y_(N, v) (Y _(v,Γ) ^(H)Y v,Γ)⁻¹Y v,Γ^(H) can be computed and stored.

Note that there is no requirement that the training symbols alwaysreside in the same bins from burst to burst. As long as the transmitterand receiver both know where the training symbols are placed in anygiven burst, the training bins may be varied from one burst to the next.This may be useful to characterize the nature of colored (across SOPbins) noise and/or interference are present.

A highly advantageous simplification of (83) can be done when v trainingsymbols are placed in bins that are evenly spaced throughout the burst.In other words,$J = {\left\{ {0,\frac{N}{\nu},\frac{2N}{\nu},\ldots\quad,\frac{\left( {\nu - 1} \right)N}{\nu}} \right\}.}$In this case, Y_(J, v) ⁻¹ is equal to the v-point IFFT matrix so thatequation (81) represents the execution of an v-point IFFT. One may thenobtain Ĥ_(i) in equation (82) by performing an N-point FFT on a vectorconsisting of ĥ_(i) padded with N−v zeros. This approach to identifyingĤ_(i) is only of computation order (N+v)log₂ v.Identification Over Multiple Bursts

Identification accuracy can be improved by either increasing the numberof training symbols within each burst or by averaging over multiplebursts if the channel is correlated from one burst to another. Somedegree of time domain correlation exists in the channel because theDoppler frequency shifts caused by moving objects in the physicalenvironment are band-limited. This time correlation can be exploited byrecursively filtering the estimated channel from the present burst withchannel estimates from previous bursts. A general filtering approach isrepresented by{tilde over (h)}(k+1)=F(k){tilde over (h)}(k)+G(k)ĥ(k)

where {tilde over (h)} is the smoothed channel estimate of ĥ over burstsk. The particular recursive filter weights F(k) and G(k) can be derivedin a number of fashions. Two exemplary filtering methods are given inthe following. The first approach determines a time-invariant FIR filterfor each element of h based on a MMSE cost function. The second designis time-varying Kalman filter.

A particularly simple, yet effective, filter design technique is thedetermination of a time-invariant FIR filter, w, that minimizes the MMSEbetween the true channel impulse response and the filtered estimate.This design approach is referred to as Wiener filtering. In thisembodiment, independent fading is assumed on each element of the channelimpulse response. Therefore, each element of h can be consideredindependently. An FIR filter produces a filtered estimate by forming aweighted sum of the previous p+1 estimates for that particular impulseresponse element, $\begin{matrix}{{{{\overset{\sim}{h}}_{i}(k)} = {w^{H}\begin{bmatrix}\begin{matrix}{{\hat{h}}_{i}(k)} \\\vdots\end{matrix} \\{{\hat{h}}_{i}\left( {k - p} \right)}\end{bmatrix}}},} \\{{{\forall i} = 1},2,\ldots\quad,{\nu.}}\end{matrix}$

Using v such identical filters for each element of the impulse response,then the filtered estimate is given by {tilde over (h)}(k)=[{tilde over(h)}₁(k) . . . {tilde over (h)}_(v)(k)]^(T). The Wiener filter solutionfor w satisfies the following equation,${\underset{w}{\min\quad}{E\left( {{{w^{H}{\hslash_{i}(k)}} - {h_{i}(k)}}}^{2} \right)}} = {\underset{w}{\min\quad}{{E\left( {{{w^{H}\begin{bmatrix}\begin{matrix}{{\hat{h}}_{i}(k)} \\\vdots\end{matrix} \\{{\hat{h}}_{i}\left( {k - p} \right)}\end{bmatrix}} - {h_{i}(k)}}}^{2} \right)}.}}$

The solution for the above optimization problem is given by,w=[E( h _(i)(k) h _(i)(k)^(H))]⁻¹ E[ h _(i)(k) h _(i)(k)]=R _(h) _(i) ⁻¹R _(h) _(i) _(h) _(i) .

If each delay in the channel impulse response undergoes Raleigh fadingis assumed then,$R_{\hslash_{i}} = {{\sigma_{h}^{2}\left\lbrack {\begin{matrix}\begin{matrix}\begin{matrix}{J_{0}(0)} \\{J_{0}\left( {{\omega\left( {N + \nu} \right)}T} \right)}\end{matrix} \\\vdots\end{matrix} \\{J_{0}\left( {\omega\quad{p\left( {N + \nu} \right)}T} \right)}\end{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{J_{0}\left( {\omega\quad\left( {N + \nu} \right)T} \right)} \\⋰\end{matrix} \\\quad\end{matrix} \\\cdots\end{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\cdots \\\quad\end{matrix} \\⋰\end{matrix} \\\quad\end{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{J_{0}\left( {\omega\quad\left( {N + \nu} \right)T} \right)} \\\vdots\end{matrix} \\\quad\end{matrix} \\{J_{0}(0)}\end{matrix}} \right\rbrack} + {\sigma_{e}^{2}I}}$ and${R_{\hslash_{i}h} = {\sigma_{h}^{2}\begin{bmatrix}\begin{matrix}\begin{matrix}{J_{0}(0)} \\{J_{0}\left( {{\omega\left( {N + \nu} \right)}T} \right)}\end{matrix} \\\vdots\end{matrix} \\{J_{0}\left( {\omega\quad{p\left( {N + \nu} \right)}T} \right)}\end{bmatrix}}},$

where T is the sampling rate, ω is the maximum Doppler frequency, and J₀is the zeroth-order Bessel function. The quantities σ_(h) ² and σ_(e) ²are the average channel power and the channel estimation noise power,respectively.

This filtering approach has many advantages. First, it iscomputationally simple. Each coefficient of the channel impulse responseis filtered independently with a constant, precomputed FIR weighting.Second, the underlying time-correlation in the multipath fading channelis efficiently exploited. Third, the exact values used for the filterare optimal in a MMSE sense.

A more generalized time-varying filtering approach is now developedbased on the Kalman filtering equations. A general model for thetime-correlated nature of the channel impulse response is given by thefollowing set of equations,f(k+1)=Af(k)+q(k){tilde over (h)}(k)=Cf(k)+r(k)

where the q and r represent noises with covariances Q and R,respectively. The matrices A,C,Q,R are used to define the particularmodel for the correlation of the impulse response over bursts. Note thatthe vector {tilde over (h)} can also include the impulse responsecoefficients for more than one receive antenna. In this case, the abovemodel can include both time correlation and correlation across space.

In a multi-access scheme, successive channel identifications may occurat an irregular rate. In this case, this Kalman filter approach isparticularly useful since the filtering can be done with measurementupdates and time updates,{circumflex over (f)}(k+1)=A(I−L(k)C){circumflex over (f)}(k)+AL(k)ĥ(k)L(k)={circumflex over (P)}(k)C ^(H)(C{circumflex over (P)}(k)C ^(H)+R)⁻¹{circumflex over (P)}(k)=A(I−L(k)C){circumflex over (P)}(k)A ^(H) +Q{tilde over (h)}(k)=C{circumflex over (f)}(k)

where L(k)=0 when the receiver is not receiving data in the presentburst.

Interference Subspace Identification

For many of the spatial processing techniques embodied in thisinvention, the operation of the TSP and RSP can depend, in part, on thelevel of interference present in the wireless environment within whichthe invention operates. More specifically, it may be preferable toreduce the amount of interference contributed to other receivers by ajudicious choice of the TSWs. It may also be preferable to improve thesignal quality at the receiver by using RSWs that reject interference.In these cases, some quantitative measure of the interference acrossspace and frequency is needed.

One preferable measure of the interference present is the so-calledinterference spatial covariance matrix, which describes interferencecorrelation across space for each frequency bin,R _(I)(n)=E[I(n)I(n)^(H)],  (1)

where x_(I)(n) represents an M_(R)-length received vector of signalsfrom the interfering transmitter(s). To be more precise, R_(I)(n)describes the interference and noise correlation across space for eachfrequency bin. Since we assume that the noise at the output of eachreceiver antenna path is additive thermal noise, and therefore that theadditive noise is uncorrelated between any two antenna outputs, thenoise contribution to R_(I)(n) is non-zero only on the matrix diagonal.In environments dominated by interference, i.e. the interference powerat the receiver is much stronger than the additive receiver noise, thenoise contribution to R_(I)(n) can be neglected. The interferencecovariance matrix contains information about the average spatialbehavior of the interference. The eigenvectors of this matrix define theaverage spatial directions (in M_(R)-space) occupied by theinterference. The eigenvalues of the matrix indicate the average poweroccupied by the interference in each the eigendirection. Theeigendirections that are associated with large eigenvalues indicatespatial directions that receive a large amount of average interferencepower. The eigendirections associated with small eigenvalues indicatespatial directions that are preferable in that they receive less averageinterference power.

Identifying the receive covariance matrix, R_(I)(n), is required forfinding preferable RSPs. An analogous transmit covariance matrix isrequired for finding preferable TSPs. Notice that we've defined R_(I)(n)in terms of received signal samples in Equation (1). Since the receivedsignal samples are not usually available at the transmitter, it ispreferable to derive the transmit covariance matrix from the receivecovariance matrix. In time division duplex (TDD) systems, the receiveand transmit covariance matrices are substantially equal when the timebetween reception and transmission is short relative to the rate of timevariation in the channel. In frequency division duplex (FDD) systems,the transmit and receive channel values are generally not correlatedwith one another at any given instant in time. However, the transmit andreceive covariance matrices are substantially equal in FDD systems whensufficient time averaging is used in the calculation of R_(I). There aremany techniques for determining the interference covariance matrix, twoof which are discussed below.

One interference characterization approach simply averages the receivedantenna signals during time periods in which the desired transceiver isnot transmitting information. Since there is no desired signal arrivingat the receiver, the interference (and noise) covariance is preciselyequal to the measured sample covariance matrix, $\begin{matrix}{{{\hat{R}}_{I}(n)} = {{\hat{R}}_{x}(n)}} \\{= {\frac{1}{k_{2} - k_{1}}{\sum\limits_{j = k_{1}}^{k_{2}}{{x\left( {n,j} \right)}{{x\left( {n,j} \right)}^{H}.}}}}}\end{matrix}$

In TDD systems, one can make use of “dead-time” to collect samples fromthe receiver during which time no energy from the transmitting endarrives at the receiver. The “dead-time” is approximately equal to theround trip propagation delay between the to ends of the wirelesscommunications link, and occurs when a transceiver switches fromtransmission mode to reception mode. In the above equation, k₁ and k₂are the burst indexes corresponding to the first and last burstsreceived during the dead time. Thus, the interference covariance can beestimated with no increase in overhead.

The interference covariance matrices can also be determined while thedesired signal is being transmitted to the receiver. One approachinvolves first determining the interference signal and subsequentlyfinding the interference signal covariance. The estimated receivedinterference is formed by subtracting the estimated desired signal fromthe total received signal,I (n,k)=x(n,k)−Ĥ(n,k){circumflex over (z)}(n,k).

Therefore, once the channel is identified and the information symbolsdetermined, the remaining signal is considered to be interference. Theinterference covariance matrix for bin n, averaged over K bursts isgiven by,${R_{I}\left( {n,k} \right)} = {\frac{1}{K}{\sum\limits_{j = {k - K + 1}}^{k}{{\hat{I}\left( {n,k} \right)}{{\hat{I}\left( {n,k} \right)}^{H}.}}}}$

It is understood that when estimating the covariance matrix, it may bedesirable to filter the covariance matrix estimates. It may also beadvantageous in certain embodiments to determine an average interferencecovariance matrix across SOP bins. For example, within a multiple accesssystem bursts may only be received occasionally, making it difficult toacquire a sufficient number of bursts with which to form an accuratecovariance matrix for each bin. So instead of averaging over time (aseries of received bursts), a covariance matrix is formed by averagingover the SOP bins of a single burst,${R_{I}(k)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}{{\hat{I}\left( {n,k} \right)}{{\hat{I}\left( {n,k} \right)}^{H}.}}}}$

It may also be preferable to estimate the interference covariancematrices in an alternate frequency band. This can be done using the“dead-time” approach given above. This may be advantageous when thetransceiver has the capability of choosing alternate frequency bands forcommunicating. Estimates of interference in alternate bands provides thefoundation for an adaptive frequency hopped scheme.

It is understood that the examples and embodiments described herein arefor illustrative purposes only and that various modifications or changesin light thereof will be suggested to persons skilled in the art and areto be included within the spirit and purview of this application andscope of the appended claims and their full scope of equivalents. Forexample, much of the above discussion concerns signal processing in thecontext of a wireless communication system where multiple inputs ormultiple outputs are accessed by multiple transmitter antenna elementsor multiple receiver antenna elements. However, the present invention isalso useful in the context of wireline channels accessible via multipleinputs or multiple outputs.

1. A method for operating a transmitter to transmit into a channel via aplurality of antenna elements, said method comprising: establishing aplurality of orthogonal frequency bins; establishing a plurality ofspatial subchannels, each of said spatial subchannels corresponding to afrequency bin and to transmission via exactly one of said antennaelements; for at least one of said plurality of orthogonal frequencybins, dividing information among said plurality of spatial subchannels;and transmitting information via said plurality of spatial subchannelsin accordance with said dividing.
 2. An apparatus for operating atransmitter to transmit into a channel via a plurality of antennaelements, said apparatus comprising: means for establishing a pluralityof orthogonal frequency bins; means for establishing a plurality ofspatial subchannels, each of said spatial subchannels corresponding to afrequency bin and to transmission via exactly one of said antennaelements; means for dividing information among said plurality of spatialsubchannels for at least one of said plurality of orthogonal frequencybins; and means for transmitting information via said plurality ofspatial subchannels in accordance with said dividing of said means fordividing.
 3. An apparatus for operating a transmitter to transmit into achannel via a plurality of antenna elements, said apparatus comprising:a frequency domain processor that establishes a plurality of orthogonalfrequency bins; and a spatial processor arranged to establish, for atleast one of said orthogonal frequency bins, a plurality of spatialsubchannels, each of said spatial subchannels corresponding totransmission of said frequency bin via exactly one of said antennaelements and, for at least one of said plurality of orthogonal frequencybins, the spatial processor further arranged to divide information amongsaid plurality of spatial subchannels; and wherein information istransmitted via said plurality of subchannels in accordance with saiddividing.
 4. A method for operating a receiver to receive from a channelvia a plurality of antenna elements, said method comprising:establishing a plurality of orthogonal frequency bins; establishing aplurality of spatial subchannels, each of said spatial subchannelscorresponding to reception of a frequency bin via exactly one of saidantenna elements; for at least one of said plurality of orthogonalfrequency bins, receiving information via said plurality of spatialsubchannels.